Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5001	Find the Characteristic Equation	[[-2,6,-7],[3,-9,10],[-1,3,-3]]	$[\begin{array}{c} - 2 & 6 & - 7 \\ 3 & - 9 & 10 \\ - 1 & 3 & - 3 \end{array}]$
5002	Find the Characteristic Equation	[[3,-1],[2,0]]	$[\begin{array}{c} 3 & - 1 \\ 2 & 0 \end{array}]$
5003	Find the Characteristic Equation	[[3,2],[3,-2]]	$[\begin{array}{c} 3 & 2 \\ 3 & - 2 \end{array}]$
5004	Find the Eigenvectors/Eigenspace	a=[[8,-6,2],[-6,7,-4],[2,-4,3]]	$a = [\begin{array}{c} 8 & - 6 & 2 \\ - 6 & 7 & - 4 \\ 2 & - 4 & 3 \end{array}]$
5005	Find the Eigenvectors/Eigenspace	A=[[cos(o),-sin(o)],[sin(o),cos(o)]]	$A = [\begin{array}{c} \cos (o) & - \sin (o) \\ \sin (o) & \cos (o) \end{array}]$
5006	Find the Eigenvectors/Eigenspace	[[3,-2,4],[-10,-10,4],[-5,-1,-6]]	$[\begin{array}{c} 3 & - 2 & 4 \\ - 10 & - 10 & 4 \\ - 5 & - 1 & - 6 \end{array}]$
5007	Find the Eigenvectors/Eigenspace	[[0.8,0.3],[0.2,0.7]]	$[\begin{array}{c} 0.8 & 0.3 \\ 0.2 & 0.7 \end{array}]$
5008	Find the Eigenvectors/Eigenspace	[[0,0,0],[0,16,16],[16,1,-16]]	$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 16 & 16 \\ 16 & 1 & - 16 \end{array}]$
5009	Find the Eigenvectors/Eigenspace	[[0,1,0,-1],[1,0,-1,0],[0,-1,0,-1],[-1,0,-1,0]]	$[\begin{array}{c} 0 & 1 & 0 & - 1 \\ 1 & 0 & - 1 & 0 \\ 0 & - 1 & 0 & - 1 \\ - 1 & 0 & - 1 & 0 \end{array}]$
5010	Find the Eigenvectors/Eigenspace	[[0,4,10,0],[-1,4,5,0],[7,-14,2,0],[-12,24,6,2]]	$[\begin{array}{c} 0 & 4 & 10 & 0 \\ - 1 & 4 & 5 & 0 \\ 7 & - 14 & 2 & 0 \\ - 12 & 24 & 6 & 2 \end{array}]$
5011	Find the Eigenvectors/Eigenspace	[[0.8,0.2,0.2],[0.0,0.5,0.1],[0.2,0.3,0.7]]	$[\begin{array}{c} 0.8 & 0.2 & 0.2 \\ 0 & 0.5 & 0.1 \\ 0.2 & 0.3 & 0.7 \end{array}]$
5012	Find the Eigenvectors/Eigenspace	[[1,0,0,0],[0,1,0,0],[0,0,1,1],[0,0,1,1]]	$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 1 \\ 0 & 0 & 1 & 1 \end{array}]$
5013	Find the Eigenvectors/Eigenspace	[[1,0,0,0],[0,1,5,-10],[1,0,2,0],[1,0,0,3]]	$[\begin{array}{c} 1 & 0 & 0 & 0 \\ 0 & 1 & 5 & - 10 \\ 1 & 0 & 2 & 0 \\ 1 & 0 & 0 & 3 \end{array}]$
5014	Find the Eigenvectors/Eigenspace	[[-1,0,0,1],[0,-1,1,0],[0,1,-1,0],[1,0,0,-1]]	$[\begin{array}{c} - 1 & 0 & 0 & 1 \\ 0 & - 1 & 1 & 0 \\ 0 & 1 & - 1 & 0 \\ 1 & 0 & 0 & - 1 \end{array}]$
5015	Find the Characteristic Equation	[[40,-84,0],[18,-38,0],[36,-72,-2]]	$[\begin{array}{c} 40 & - 84 & 0 \\ 18 & - 38 & 0 \\ 36 & - 72 & - 2 \end{array}]$
5016	Find the Characteristic Equation	[[5,0],[2,-2]]	$[\begin{array}{c} 5 & 0 \\ 2 & - 2 \end{array}]$
5017	Find the Characteristic Equation	[[5,1,2],[0,1,0],[2,1,4]]	$[\begin{array}{c} 5 & 1 & 2 \\ 0 & 1 & 0 \\ 2 & 1 & 4 \end{array}]$
5018	Find the Characteristic Equation	[[9,9],[7,8]]	$[\begin{array}{c} 9 & 9 \\ 7 & 8 \end{array}]$
5019	Find the Characteristic Equation	[[h,0],[1,-2]]	$[\begin{array}{c} h & 0 \\ 1 & - 2 \end{array}]$
5020	Find the Eigenvectors/Eigenspace	A=[[0,7],[1/7,0]]	$A = [\begin{array}{c} 0 & 7 \\ \frac{1}{7} & 0 \end{array}]$
5021	Find the Characteristic Equation	[[17,22,4],[2,9,11],[4,6,13]]	$[\begin{array}{c} 17 & 22 & 4 \\ 2 & 9 & 11 \\ 4 & 6 & 13 \end{array}]$
5022	Find the Characteristic Equation	[[19,25,30,5],[-23,-30,-35,-5],[7,9,10,1],[-3,-4,-5,-1]]	$[\begin{array}{c} 19 & 25 & 30 & 5 \\ - 23 & - 30 & - 35 & - 5 \\ 7 & 9 & 10 & 1 \\ - 3 & - 4 & - 5 & - 1 \end{array}]$
5023	Find the Characteristic Equation	[[2,3,-1,0],[1,2,4,3],[-2,1,3,2],[-1,-2,-3,0]]	$[\begin{array}{c} 2 & 3 & - 1 & 0 \\ 1 & 2 & 4 & 3 \\ - 2 & 1 & 3 & 2 \\ - 1 & - 2 & - 3 & 0 \end{array}]$
5024	Find the Characteristic Equation	[[-2,-4,2,-2],[1,5,5,-8],[-1,0,7,-11],[2,7,3,-3]]	$[\begin{array}{c} - 2 & - 4 & 2 & - 2 \\ 1 & 5 & 5 & - 8 \\ - 1 & 0 & 7 & - 11 \\ 2 & 7 & 3 & - 3 \end{array}]$
5025	Find the Eigenvalues	[[-2,1,-2,-4],[12,1,4,9],[6,5,-2,-4],[3,-4,5,10]]	$[\begin{array}{c} - 2 & 1 & - 2 & - 4 \\ 12 & 1 & 4 & 9 \\ 6 & 5 & - 2 & - 4 \\ 3 & - 4 & 5 & 10 \end{array}]$
5026	Find the Eigenvalues	[[-1,-1],[0,-0.25]]	$[\begin{array}{c} - 1 & - 1 \\ 0 & - 0.25 \end{array}]$
5027	Find the Cofactor Matrix	[[5,-4,4],[3,5,5],[9,10,6]]	$[\begin{array}{c} 5 & - 4 & 4 \\ 3 & 5 & 5 \\ 9 & 10 & 6 \end{array}]$
5028	Find the Cofactor Matrix	[[6,4,2],[5,1,8],[6,8,7]]	$[\begin{array}{c} 6 & 4 & 2 \\ 5 & 1 & 8 \\ 6 & 8 & 7 \end{array}]$
5029	Find the Cofactor Matrix	[[6,-7],[8,-9]]	$[\begin{array}{c} 6 & - 7 \\ 8 & - 9 \end{array}]$
5030	Find the Cofactor Matrix	[[6e^(-4x),0,-3],[12e^(-4x),9e^(-2x),-15],[3e^(-4x),3e^(-2x),-3]]	$[\begin{array}{c} 6 e^{- 4 x} & 0 & - 3 \\ 12 e^{- 4 x} & 9 e^{- 2 x} & - 15 \\ 3 e^{- 4 x} & 3 e^{- 2 x} & - 3 \end{array}]$
5031	Find the Cofactor Matrix	[[a-b,b+c],[-3d+c,2a-4d]]	$[\begin{array}{c} a - b & b + c \\ - 3 d + c & 2 a - 4 d \end{array}]$
5032	Solve Using an Inverse Matrix	5a-1b=-8 , -1a+5b=16	$5 a - 1 b = - 8$ , $- 1 a + 5 b = 16$
5033	Find the Domain	4x(1)+2y=8	$4 x (1) + 2 y = 8$
5034	Solve Using an Inverse Matrix	0.06t+0.065b=632.5 , t+b=10000	$0.06 t + 0.065 b = 632.5$ , $t + b = 10000$
5035	Solve Using an Inverse Matrix	0.3x+1.1y=3.5 , -0.5x-2.9y=-10.1	$0.3 x + 1.1 y = 3.5$ , $- 0.5 x - 2.9 y = - 10.1$
5036	Solve Using an Inverse Matrix	-0.63x+y=0.52 , 0.44x+y=1.66	$- 0.63 x + y = 0.52$ , $0.44 x + y = 1.66$
5037	Solve Using an Inverse Matrix	1/2x-1/3y=2 , 3/4x+2y=-12	$\frac{1}{2} x - \frac{1}{3} y = 2$ , $\frac{3}{4} x + 2 y = - 12$
5038	Solve Using an Inverse Matrix	1/3y-2/3x=1 , 10x-5y=-15	$\frac{1}{3} y - \frac{2}{3} x = 1$ , $10 x - 5 y = - 15$
5039	Solve Using an Inverse Matrix	1/5x+y=6 , -4x+5y=10	$\frac{1}{5} x + y = 6$ , $- 4 x + 5 y = 10$
5040	Solve Using an Inverse Matrix	1/x+1/y=6 , -1/y+2/z=-2 , 1/z-3/x=4	$\frac{1}{x} + \frac{1}{y} = 6$ , $\frac{- 1}{y} + \frac{2}{z} = - 2$ , $\frac{1}{z} - \frac{3}{x} = 4$
5041	Solve Using an Inverse Matrix	3^2a+3b+c=4 , 5^2a+5b+c=4 , 2^2a+2b+c=1	$3^{2} a + 3 b + c = 4$ , $5^{2} a + 5 b + c = 4$ , $2^{2} a + 2 b + c = 1$
5042	Solve Using an Inverse Matrix	x^2+y^2=40 , x^2-y^2=-32	$x^{2} + y^{2} = 40$ , $x^{2} - y^{2} = - 32$
5043	Solve Using an Inverse Matrix	x^2-300x+(-y^2)/(1.22^2)=0 , y=3x-600	$x^{2} - 300 x + \frac{- y^{2}}{{1.22}^{2}} = 0$ , $y = 3 x - 600$
5044	Solve Using an Inverse Matrix	0.6x-0.2y=-0.2 , -0.03x-0.07y=0.17	$0.6 x - 0.2 y = - 0.2$ , $- 0.03 x - 0.07 y = 0.17$
5045	Solve Using an Inverse Matrix	0.9x+y=1.2 , 2.4x-3y=8.1	$0.9 x + y = 1.2$ , $2.4 x - 3 y = 8.1$
5046	Solve Using an Inverse Matrix	-0.9x-0.8y=-0.5 , 0.08(y+0.5)=-0.09x	$- 0.9 x - 0.8 y = - 0.5$ , $0.08 (y + 0.5) = - 0.09 x$
5047	Solve Using an Inverse Matrix	1.5x-y=-2 , -5x+4y=14	$1.5 x - y = - 2$ , $- 5 x + 4 y = 14$
5048	Solve Using an Inverse Matrix	10x+3y=66 , 8x+3y=54	$10 x + 3 y = 66$ , $8 x + 3 y = 54$
5049	Solve Using an Inverse Matrix	11x+2y=-13 , 2x-y=-1	$11 x + 2 y = - 13$ , $2 x - y = - 1$
5050	Solve Using an Inverse Matrix	11x-9y=-4 , 6x-5y=-3	$11 x - 9 y = - 4$ , $6 x - 5 y = - 3$
5051	Solve Using an Inverse Matrix	12x-3y=-6 , 2x+12y=24	$12 x - 3 y = - 6$ , $2 x + 12 y = 24$
5052	Solve Using an Inverse Matrix	12x+4=8y , y=x-7	$12 x + 4 = 8 y$ , $y = x - 7$
5053	Solve Using an Inverse Matrix	12x-3y=-6 , 2x+15y=30	$12 x - 3 y = - 6$ , $2 x + 15 y = 30$
5054	Solve Using an Inverse Matrix	13+2y=9x , 3y=7x	$13 + 2 y = 9 x$ , $3 y = 7 x$
5055	Solve Using an Inverse Matrix	-13x=97-19y , -17x=83+19y	$- 13 x = 97 - 19 y$ , $- 17 x = 83 + 19 y$
5056	Solve Using an Inverse Matrix	14x-21y-7z=10 , -4x+2y-2z=4 , 56x-21y+7z=5	$14 x - 21 y - 7 z = 10$ , $- 4 x + 2 y - 2 z = 4$ , $56 x - 21 y + 7 z = 5$
5057	Solve Using an Inverse Matrix	15x+5y=4 , -3x=y+6	$15 x + 5 y = 4$ , $- 3 x = y + 6$
5058	Solve Using an Inverse Matrix	-16y=22+6x , -11y-4x=15	$- 16 y = 22 + 6 x$ , $- 11 y - 4 x = 15$
5059	Solve Using an Inverse Matrix	2(x-y)=180 , 1.5(x+y)=180	$2 (x - y) = 180$ , $1.5 (x + y) = 180$
5060	Solve Using an Inverse Matrix	200x+528y+242z=1854 , 8x+24y+11z=81 , 4x+48y+33z=159	$200 x + 528 y + 242 z = 1854$ , $8 x + 24 y + 11 z = 81$ , $4 x + 48 y + 33 z = 159$
5061	Solve Using an Inverse Matrix	-21x-2y+z=-76 , 12x+y=46 , -24x-2y+z=-88	$- 21 x - 2 y + z = - 76$ , $12 x + y = 46$ , $- 24 x - 2 y + z = - 88$
5062	Solve Using an Inverse Matrix	25x+30y+30z=1475 , 50x+30y+20z=990 , 75x+30y+20z=810	$25 x + 30 y + 30 z = 1475$ , $50 x + 30 y + 20 z = 990$ , $75 x + 30 y + 20 z = 810$
5063	Find the Cofactor Matrix	[[1,2,-1],[3,-3,2],[-1,-11,6]]	$[\begin{array}{c} 1 & 2 & - 1 \\ 3 & - 3 & 2 \\ - 1 & - 11 & 6 \end{array}]$
5064	Find the Cofactor Matrix	[[1,2,3,4],[6,7,8,9],[1,2,-3,4],[-6,-7,-8,-9]]	$[\begin{array}{c} 1 & 2 & 3 & 4 \\ 6 & 7 & 8 & 9 \\ 1 & 2 & - 3 & 4 \\ - 6 & - 7 & - 8 & - 9 \end{array}]$
5065	Find the Cofactor Matrix	[[1,2,3],[1,1,2],[0,1,2]]	$[\begin{array}{c} 1 & 2 & 3 \\ 1 & 1 & 2 \\ 0 & 1 & 2 \end{array}]$
5066	Find the Cofactor Matrix	[[1,2,3],[2,3,3],[4,6,5]]	$[\begin{array}{c} 1 & 2 & 3 \\ 2 & 3 & 3 \\ 4 & 6 & 5 \end{array}]$
5067	Find the Cofactor Matrix	[[1,3,-2],[3,9,-6],[-2,-6,4]]	$[\begin{array}{c} 1 & 3 & - 2 \\ 3 & 9 & - 6 \\ - 2 & - 6 & 4 \end{array}]$
5068	Find the Cofactor Matrix	[[1,3,4],[-2,-6,-8],[1,4,9]]	$[\begin{array}{c} 1 & 3 & 4 \\ - 2 & - 6 & - 8 \\ 1 & 4 & 9 \end{array}]$
5069	Find the Cofactor Matrix	[[-1,-4,-7],[-10,-13,-16],[-19,-22,-25]]	$[\begin{array}{c} - 1 & - 4 & - 7 \\ - 10 & - 13 & - 16 \\ - 19 & - 22 & - 25 \end{array}]$
5070	Find the Cofactor Matrix	[[17,22,4],[2,9,11],[4,6,13]]	$[\begin{array}{c} 17 & 22 & 4 \\ 2 & 9 & 11 \\ 4 & 6 & 13 \end{array}]$
5071	Find the Cofactor Matrix	[[2,1],[3,2]]	$[\begin{array}{c} 2 & 1 \\ 3 & 2 \end{array}]$
5072	Find the Cofactor Matrix	[[2,-3,3],[2,1,1],[1,5,-1]]	$[\begin{array}{c} 2 & - 3 & 3 \\ 2 & 1 & 1 \\ 1 & 5 & - 1 \end{array}]$
5073	Find the Cofactor Matrix	[[-3,4,x],[5,0,0],[2,1,2]]	$[\begin{array}{c} - 3 & 4 & x \\ 5 & 0 & 0 \\ 2 & 1 & 2 \end{array}]$
5074	Find the Cofactor Matrix	[[3,-8],[4,6]]	$[\begin{array}{c} 3 & - 8 \\ 4 & 6 \end{array}]$
5075	Find the Cofactor Matrix	[[4,0,-1],[0,4,-1],[1,0,2]]	$[\begin{array}{c} 4 & 0 & - 1 \\ 0 & 4 & - 1 \\ 1 & 0 & 2 \end{array}]$
5076	Find the Cofactor Matrix	[[4,10,30],[10,30,100],[30,100,354]]	$[\begin{array}{c} 4 & 10 & 30 \\ 10 & 30 & 100 \\ 30 & 100 & 354 \end{array}]$
5077	Find the Cofactor Matrix	[[-4,3,4],[1,4,-3],[2,-4,1]]	$[\begin{array}{c} - 4 & 3 & 4 \\ 1 & 4 & - 3 \\ 2 & - 4 & 1 \end{array}]$
5078	Find the Cofactor Matrix	[[5,-2],[-2,2]]	$[\begin{array}{c} 5 & - 2 \\ - 2 & 2 \end{array}]$
5079	Evaluate	(-2+ square root of 8)/(-3- square root of 2)	$\frac{- 2 + \sqrt{8}}{- 3 - \sqrt{2}}$
5080	Evaluate	(2i square root of 5)/(i square root of 2)	$\frac{2 i \sqrt{5}}{i \sqrt{2}}$
5081	Evaluate	59/(1 square root of 6)	$\frac{59}{1 \sqrt{6}}$
5082	Evaluate	65160/( square root of 71.87x square root of 923.25)	$\frac{65160}{\sqrt{71.87} x \sqrt{923.25}}$
5083	Evaluate	69465/( square root of 56565)	$\frac{69465}{\sqrt{56565}}$
5084	Evaluate	(8a^2b square root of c^3)/((2a)^2 square root of b square root of c)	$\frac{8 a^{2} b \sqrt{c^{3}}}{{(2 a)}^{2} \sqrt{b} \sqrt{c}}$
5085	Evaluate	8/( square root of 56-7x)	$\frac{8}{\sqrt{56 - 7 x}}$
5086	Evaluate	8/( square root of -7- square root of 3)	$\frac{8}{\sqrt{- 7} - \sqrt{3}}$
5087	Evaluate	8/( seventh root of xy^6)	$\frac{8}{\sqrt[7]{x y^{6}}}$
5088	Evaluate	-9/(8+5 square root of 7)	$\frac{- 9}{8 + 5 \sqrt{7}}$
5089	Evaluate	(a-b)/( square root of a- square root of b)	$\frac{a - b}{\sqrt{a} - \sqrt{b}}$
5090	Find the Cofactor Matrix	(2A^T)^-1=[[4,5],[3,4]]	${(2 A^{T})}^{- 1} = [\begin{array}{c} 4 & 5 \\ 3 & 4 \end{array}]$
5091	Find the Cofactor Matrix	a^-1=1/(27[[6,1,-5],[-3,-5,25],[-3,4,7]])	$a^{- 1} = \frac{1}{27 [\begin{array}{c} 6 & 1 & - 5 \\ - 3 & - 5 & 25 \\ - 3 & 4 & 7 \end{array}]}$
5092	Find the Cofactor Matrix	5[[-3,6],[0,2]]	$5 [\begin{array}{c} - 3 & 6 \\ 0 & 2 \end{array}]$
5093	Find the Cofactor Matrix	A=[[1,0,0],[-1,1,1],[-1,-2,4]]	$A = [\begin{array}{c} 1 & 0 & 0 \\ - 1 & 1 & 1 \\ - 1 & - 2 & 4 \end{array}]$
5094	Find the Cofactor Matrix	A=[[4,2],[3,3]]	$A = [\begin{array}{c} 4 & 2 \\ 3 & 3 \end{array}]$
5095	Find the Cofactor Matrix	A=[[-5,-1],[-5,4]]	$A = [\begin{array}{c} - 5 & - 1 \\ - 5 & 4 \end{array}]$
5096	Find the Cofactor Matrix	B=[[2,7],[9,10]]	$B = [\begin{array}{c} 2 & 7 \\ 9 & 10 \end{array}]$
5097	Find the Adjoint	[[4,0,-2],[2,3,4],[5,-7,6]]	$[\begin{array}{c} 4 & 0 & - 2 \\ 2 & 3 & 4 \\ 5 & - 7 & 6 \end{array}]$
5098	Find the Adjoint	[[5,-10,-5],[2,14,2],[-4,-8,6]]	$[\begin{array}{c} 5 & - 10 & - 5 \\ 2 & 14 & 2 \\ - 4 & - 8 & 6 \end{array}]$
5099	Find the Adjoint	[[-63,30,24],[33,-15,-9],[-45,30,15]]	$[\begin{array}{c} - 63 & 30 & 24 \\ 33 & - 15 & - 9 \\ - 45 & 30 & 15 \end{array}]$
5100	Find the Adjoint	[[8,4],[2,3]]	$[\begin{array}{c} 8 & 4 \\ 2 & 3 \end{array}]$