Linear Algebra Examples

Find the Projection of a Onto b
,
Step 1
Find the dot product.
Tap for more steps...
Step 1.1
The dot product of two vectors is the sum of the products of the their components.
Step 1.2
Simplify.
Tap for more steps...
Step 1.2.1
Simplify each term.
Tap for more steps...
Step 1.2.1.1
Multiply by .
Step 1.2.1.2
Multiply by .
Step 1.2.1.3
Multiply by .
Step 1.2.2
Add and .
Step 1.2.3
Add and .
Step 2
Find the norm of .
Tap for more steps...
Step 2.1
The norm is the square root of the sum of squares of each element in the vector.
Step 2.2
Simplify.
Tap for more steps...
Step 2.2.1
One to any power is one.
Step 2.2.2
Raise to the power of .
Step 2.2.3
One to any power is one.
Step 2.2.4
Add and .
Step 2.2.5
Add and .
Step 3
Find the projection of onto using the projection formula.
Step 4
Substitute for .
Step 5
Substitute for .
Step 6
Substitute for .
Step 7
Simplify the right side.
Tap for more steps...
Step 7.1
Rewrite as .
Tap for more steps...
Step 7.1.1
Use to rewrite as .
Step 7.1.2
Apply the power rule and multiply exponents, .
Step 7.1.3
Combine and .
Step 7.1.4
Cancel the common factor of .
Tap for more steps...
Step 7.1.4.1
Cancel the common factor.
Step 7.1.4.2
Rewrite the expression.
Step 7.1.5
Evaluate the exponent.
Step 7.2
Cancel the common factor of and .
Tap for more steps...
Step 7.2.1
Factor out of .
Step 7.2.2
Cancel the common factors.
Tap for more steps...
Step 7.2.2.1
Factor out of .
Step 7.2.2.2
Cancel the common factor.
Step 7.2.2.3
Rewrite the expression.
Step 7.3
Multiply by each element of the matrix.
Step 7.4
Simplify each element in the matrix.
Tap for more steps...
Step 7.4.1
Multiply by .
Step 7.4.2
Multiply .
Tap for more steps...
Step 7.4.2.1
Combine and .
Step 7.4.2.2
Multiply by .
Step 7.4.3
Multiply by .
Enter YOUR Problem
Mathway requires javascript and a modern browser.