Mathway | Popular Problems

Popular Problems

Rank	Topic	Problem	Formatted Problem
5041	Find the Cube Roots of a Complex Number	-4-4i	$- 4 - 4 i$
5042	Simplify the Matrix	(3a^2b^-4)/(12a^-2b^-2) , a!=0 , b!=0	$\frac{3 a^{2} b^{- 4}}{12 a^{- 2} b^{- 2}}$ , $a \neq 0$ , $b \neq 0$
5043	Solve using Gaussian Elimination	x+y+z=7 x-y+2z=7 2x+3z=14	$x + y + z = 7$ $x - y + 2 z = 7$ $2 x + 3 z = 14$
5044	Solve using Gaussian Elimination	2x-4y=4 x-2y=2	$2 x - 4 y = 4$ $x - 2 y = 2$
5045	Simplify the Matrix	Find DE_ifD=[[-2,4,6],[5,-7,-1]] and E=[[1,-2],[0,4],[-3,4]]	Find $D E_{i} f D = [\begin{array}{c} - 2 & 4 & 6 \\ 5 & - 7 & - 1 \end{array}]$ and $E = [\begin{array}{c} 1 & - 2 \\ 0 & 4 \\ - 3 & 4 \end{array}]$
5046	Solve using Gaussian Elimination	x+2y=5 2x+3y=6	$x + 2 y = 5$ $2 x + 3 y = 6$
5047	Simplify the Matrix	(3x^2)/(x^2-25)-x/(x+5)+2/(x-5) , x!=-5 , 5	$\frac{3 x^{2}}{x^{2} - 25} - \frac{x}{x + 5} + \frac{2}{x - 5}$ , $x \neq - 5$ , $5$
5048	Find the Norm	[[3,6,0,9,8,7]]	$[\begin{array}{c} 3 & 6 & 0 & 9 & 8 & 7 \end{array}]$
5049	Find the Fourth Roots of a Complex Number	-3+4i	$- 3 + 4 i$
5050	Simplify the Matrix	(xy^-6)/(x^-4y^2) , x!=0 , y!=0	$\frac{x y^{- 6}}{x^{- 4} y^{2}}$ , $x \neq 0$ , $y \neq 0$
5051	Simplify the Matrix	([(1,4-0,2)*3,2])÷1 , 5	$[(1, 4 - 0, 2) \cdot 3, 2] \div 1$ , $5$
5052	Solve using Gaussian Elimination	5x_1-4x_2=-8 3x_1-2x_2=-2	$5 x_{1} - 4 x_{2} = - 8$ $3 x_{1} - 2 x_{2} = - 2$
5053	Solve using Gaussian Elimination	3x_1-2x_2=28 2x_1+3x_2=-3	$3 x_{1} - 2 x_{2} = 28$ $2 x_{1} + 3 x_{2} = - 3$
5054	Solve using Gaussian Elimination	3x-5y+z=14 2x+3y-4z=20 5x-y+2z=7	$3 x - 5 y + z = 14$ $2 x + 3 y - 4 z = 20$ $5 x - y + 2 z = 7$
5055	Simplify the Matrix	(v^3w^-3)/(-v^-6w^3) , v!=0 , w!=0	$\frac{v^{3} w^{- 3}}{- v^{- 6} w^{3}}$ , $v \neq 0$ , $w \neq 0$
5056	Find the Norm	[[2],[4],[5],[6],[7]]	$[\begin{array}{c} 2 \\ 4 \\ 5 \\ 6 \\ 7 \end{array}]$
5057	Simplify the Matrix	-9/(x+3)+(x^2)/(x+3) , x!=-3	$- \frac{9}{x + 3} + \frac{x^{2}}{x + 3}$ , $x \neq - 3$
5058	Simplify the Matrix	p(x):3x/2+3\|x-2\|<=3	$p (x) : 3 \frac{x}{2} + 3 \| x - 2 \| \leq 3$
5059	Simplify the Matrix	2x-3y+z=4 y-2z+x-5=0 3-2x=4y-z	$2 x - 3 y + z = 4$ $y - 2 z + x - 5 = 0$ $3 - 2 x = 4 y - z$
5060	Simplify the Matrix	square root of 45 , square root of 125	$\sqrt{45}$ , $\sqrt{125}$
5061	Solve using Gaussian Elimination	x_1-3x_2+2x_3=5 2x_1+x_2+4x_3=24 5x_1-3x_2+x_3=-14	$x_{1} - 3 x_{2} + 2 x_{3} = 5$ $2 x_{1} + x_{2} + 4 x_{3} = 24$ $5 x_{1} - 3 x_{2} + x_{3} = - 14$
5062	Find the Cube Roots of a Complex Number	2+2i	$2 + 2 i$
5063	Simplify the Matrix	log of a+2 log of b-1/2 log of 9c^2 for a , b , c>0	$\log (a) + 2 \log (b) - \frac{1}{2} \log (9 c^{2})$ for $a$ , $b$ , $c > 0$ ?
5064	Simplify the Matrix	square root of 27 , square root of 75	$\sqrt{27}$ , $\sqrt{75}$
5065	Simplify the Matrix	B=[[-1,4,6],[-5,-3,-9]] , A=[[-4,9,2],[12,-7,-4]]	$B = [\begin{array}{c} - 1 & 4 & 6 \\ - 5 & - 3 & - 9 \end{array}]$ , $A = [\begin{array}{c} - 4 & 9 & 2 \\ 12 & - 7 & - 4 \end{array}]$
5066	Simplify the Matrix	cube root of 40 , cube root of 135	$\sqrt[3]{40}$ , $\sqrt[3]{135}$
5067	Solve using Gaussian Elimination	3x-2y+8z=38 6x+3y-9z=-12 4x+4y+20z=0	$3 x - 2 y + 8 z = 38$ $6 x + 3 y - 9 z = - 12$ $4 x + 4 y + 20 z = 0$
5068	Simplify the Matrix	square root of x^18 where x<0	$\sqrt{x^{18}}$ where $x < 0$
5069	Solve using Gaussian Elimination	x_1-3x_2+4x_3=7 2x_1+5x_2-x_3=1 3x_1-4x_2+5x_3=18	$x_{1} - 3 x_{2} + 4 x_{3} = 7$ $2 x_{1} + 5 x_{2} - x_{3} = 1$ $3 x_{1} - 4 x_{2} + 5 x_{3} = 18$
5070	Solve using Gaussian Elimination	x+3y+6z=20 2x-3y+3z=4	$x + 3 y + 6 z = 20$ $2 x - 3 y + 3 z = 4$
5071	Solve the Matrix Equation	2[[2,1],[-1,3]]+[[-6,2p],[4,-1]]=[[2,-1],[1,1]][[0,1],[2,4]]	$2 [\begin{array}{c} 2 & 1 \\ - 1 & 3 \end{array}] + [\begin{array}{c} - 6 & 2 p \\ 4 & - 1 \end{array}] = [\begin{array}{c} 2 & - 1 \\ 1 & 1 \end{array}] [\begin{array}{c} 0 & 1 \\ 2 & 4 \end{array}]$
5072	Simplify the Matrix	What is B if A=[[3,-2],[1,-4]] and AB=[[-4,-6],[2,-12]] ?	What is $B$ if $A = [\begin{array}{c} 3 & - 2 \\ 1 & - 4 \end{array}]$ and $A B = [\begin{array}{c} - 4 & - 6 \\ 2 & - 12 \end{array}]$ ?
5073	Solve using Gaussian Elimination	3x-3y-6z=3 2x-3y-5z=8 x+4y+2z=6	$3 x - 3 y - 6 z = 3$ $2 x - 3 y - 5 z = 8$ $x + 4 y + 2 z = 6$
5074	Solve Using a Matrix by Row Operations	x+y-2z+4t=5 2x+2y-3z+t=3 3x+3y-4z-2t=1	$x + y - 2 z + 4 t = 5$ $2 x + 2 y - 3 z + t = 3$ $3 x + 3 y - 4 z - 2 t = 1$
5075	Find Reduced Row Echelon Form	[[n,-8,6],[1,2,3]]	$[\begin{array}{c} n & - 8 & 6 \\ 1 & 2 & 3 \end{array}]$
5076	Simplify the Matrix	(m^7n^3)/(mn^-1) , m!=0 , n!=0	$\frac{m^{7} n^{3}}{m n^{- 1}}$ , $m \neq 0$ , $n \neq 0$
5077	Simplify the Matrix	A=[[2,3],[4,7]] and B=[[7/2,-3/2],[-2,1]]	$A = [\begin{array}{c} 2 & 3 \\ 4 & 7 \end{array}]$ and $B = [\begin{array}{c} \frac{7}{2} & - \frac{3}{2} \\ - 2 & 1 \end{array}]$
5078	Simplify the Matrix	x=x/(1-1/(1+x/y))	$x = \frac{x}{1 - \frac{1}{1 + \frac{x}{y}}}$
5079	Solve the Matrix Equation	[[12,6],[2y-1,-1.5]]=[[12,6],[-8,-1.5]]	$[\begin{array}{c} 12 & 6 \\ 2 y - 1 & - 1.5 \end{array}] = [\begin{array}{c} 12 & 6 \\ - 8 & - 1.5 \end{array}]$
5080	Solve using Gaussian Elimination	2x_1+3x_2-8x_3=105 -x_1+x_2-x_3=10 8x_1-5x_2+3x_3=-10	$2 x_{1} + 3 x_{2} - 8 x_{3} = 105$ $- x_{1} + x_{2} - x_{3} = 10$ $8 x_{1} - 5 x_{2} + 3 x_{3} = - 10$
5081	Simplify the Matrix	p(x):x+\|1+x\|=-2 q(x):2\|x+4\|-4=x	$p (x) : x + \| 1 + x \| = - 2$ $q (x) : 2 \| x + 4 \| - 4 = x$
5082	Simplify the Matrix	(-21v^6)/(-6v^8) , v!=0	$\frac{- 21 v^{6}}{- 6 v^{8}}$ , $v \neq 0$
5083	Solve using Gaussian Elimination	3x-2y-z=4 x-y-2z=0 4x+3y+z=2	$3 x - 2 y - z = 4$ $x - y - 2 z = 0$ $4 x + 3 y + z = 2$
5084	Find the Fourth Roots of a Complex Number	4+4i	$4 + 4 i$
5085	Solve using Gaussian Elimination	-x+3y+10z=8 4x-9y-34z=-17 3x+5y-2z=46	$- x + 3 y + 10 z = 8$ $4 x - 9 y - 34 z = - 17$ $3 x + 5 y - 2 z = 46$
5086	Find the Union	C={x\|x>3} D={x\|x<=8}	$C = {x \| x > 3}$ $D = {x \| x \leq 8}$
5087	Solve using Gaussian Elimination	x-y+2z=2 2y-4z=8 -x+4z=-10	$x - y + 2 z = 2$ $2 y - 4 z = 8$ $- x + 4 z = - 10$
5088	Solve Using an Augmented Matrix	4w-5x+7z=-11 -w+8x+3y=6 15x-2y+10z=9	$4 w - 5 x + 7 z = - 11$ $- w + 8 x + 3 y = 6$ $15 x - 2 y + 10 z = 9$
5089	Simplify the Matrix	-2u[[7u,3w^2,5u,5]]	$- 2 u [\begin{array}{c} 7 u & 3 w^{2} & 5 u & 5 \end{array}]$
5090	Simplify the Matrix	(-5w^4y^-2)/(-15w^-6y^2) , w!=0 , y!=0	$\frac{- 5 w^{4} y^{- 2}}{- 15 w^{- 6} y^{2}}$ , $w \neq 0$ , $y \neq 0$
5091	Simplify the Matrix	(2a^4)^-3 , a!=0	${(2 a^{4})}^{- 3}$ , $a \neq 0$
5092	Simplify the Matrix	x^3+4x^2-11x-30=(x+2)(x-3)(x+5)=0	$x^{3} + 4 x^{2} - 11 x - 30 = (x + 2) (x - 3) (x + 5) = 0$
5093	Simplify the Matrix	(((23)/9)÷3)^-2(9/4)^2(3/5)^-1	${((\frac{2 \cdot 3}{9}) \div 3)}^{- 2} {(\frac{9}{4})}^{2} \cdot {(\frac{3}{5})}^{- 1}$
5094	Simplify the Matrix	[[0,5],[-3,1],[-5,1]]*[[-4,4],[-2,-4]]	$[\begin{array}{c} 0 & 5 \\ - 3 & 1 \\ - 5 & 1 \end{array}] \cdot [\begin{array}{c} - 4 & 4 \\ - 2 & - 4 \end{array}]$
5095	Solve using Gaussian Elimination	2x+3y-z=2 3x+5y+z=4	$2 x + 3 y - z = 2$ $3 x + 5 y + z = 4$
5096	Solve using Gaussian Elimination	x-2y-z=2 2x+y-3z=4 -2x+4y+2z=6	$x - 2 y - z = 2$ $2 x + y - 3 z = 4$ $- 2 x + 4 y + 2 z = 6$
5097	Solve using Gaussian Elimination	x+3y+6z=19 2x-3y+3z=2	$x + 3 y + 6 z = 19$ $2 x - 3 y + 3 z = 2$
5098	Solve using Gaussian Elimination	x+2y+z=10 3x+7y+6z=36	$x + 2 y + z = 10$ $3 x + 7 y + 6 z = 36$
5099	Solve using Gaussian Elimination	3x_1-2x_2+x_3=-1 -x_1-x_2+6x_3=29 5x_1-3x_2-4x_3=-25	$3 x_{1} - 2 x_{2} + x_{3} = - 1$ $- x_{1} - x_{2} + 6 x_{3} = 29$ $5 x_{1} - 3 x_{2} - 4 x_{3} = - 25$
5100	Simplify the Matrix	[[6],[-3]]*[[-5,4]]	$[\begin{array}{c} 6 \\ - 3 \end{array}] \cdot [\begin{array}{c} - 5 & 4 \end{array}]$
5101	Simplify the Matrix	(x^2-4x)/(x^2-16) , x!=-4 , 4	$\frac{x^{2} - 4 x}{x^{2} - 16}$ , $x \neq - 4$ , $4$
5102	Solve using Gaussian Elimination	2x+3y-z=2 3x+5y+z=5	$2 x + 3 y - z = 2$ $3 x + 5 y + z = 5$
5103	Simplify the Matrix	(1,4-0,2) , 2	$(1, 4 - 0, 2)$ , $2$
5104	Solve using Gaussian Elimination	2x+5y-z=2 3x+8y+z=4	$2 x + 5 y - z = 2$ $3 x + 8 y + z = 4$
5105	Find the Square Roots of a Complex Number	20-21i	$20 - 21 i$
5106	Simplify the Matrix	P(x)=(x^4+2x^2+1)^2Q(x)=(x^2+34x+289)(x+1)	$P (x) = {(x^{4} + 2 x^{2} + 1)}^{2} Q (x) = (x^{2} + 34 x + 289) (x + 1)$
5107	Solve the Matrix Equation	[[4],[8],[6]]+2[[x],[y],[5z]]=[[-4],[-22],[16]]	$[\begin{array}{c} 4 \\ 8 \\ 6 \end{array}] + 2 [\begin{array}{c} x \\ y \\ 5 z \end{array}] = [\begin{array}{c} - 4 \\ - 22 \\ 16 \end{array}]$
5108	Simplify the Matrix	fourth root of 32 , fourth root of 162	$\sqrt[4]{32}$ , $\sqrt[4]{162}$
5109	Simplify the Matrix	(3x^2)(-2x^4)=3(-2)x^(2*4)=6x^8	$(3 x^{2}) (- 2 x^{4}) = 3 (- 2) x^{2 \cdot 4} = 6 x^{8}$
5110	Simplify the Matrix	square root of 8 , square root of 200	$\sqrt{8}$ , $\sqrt{200}$