IXL - Solve matrix equations using inverses (Precalculus practice)

Solve the matrix equation for

Simplify all elements.

–

If the matrix exists, select its size before entering your answer. If the matrix does not exist, select undefined.

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question

Solve the matrix equation for

Simplify all elements.

–

If the matrix exists, select its size before entering your answer. If the matrix does not exist, select undefined.

key idea

The

identity matrix

has 1's on its diagonal (upper left to lower right) and 0's elsewhere. For example:

and

The product of a matrix and the identity matrix is itself (if the product exists).

and

are

matrices and

then

is the multiplicative inverse of

written

–

A matrix is invertible if its multiplicative inverse exists.

is an invertible 2 x 2 matrix, its inverse is:

–

To find the element in the

𝑖

^th

row and

^th

column of the product of two matrices, multiply each element in the

𝑖

^th

row of the first matrix by the corresponding element in the

^th

column of the second matrix. Then add the products.

solution

To solve for

multiply both sides of the equation by the inverse of

Since the order of matrix multiplication matters, it is important that you multiply on the left of each side of the equation.

To find the inverse, follow the steps.

Since

is a 2 x 2 matrix, use the inverse formula with

and

(

)

–

(

)

–

The inverse is

–

Now, multiply by the inverse to solve for

–

So,

–

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Teacher tools

Work it out

Not feeling ready yet? These can help:

Q.12Inverse of a 2 x 2 matrix

Q.6Multiply two matrices

Q.9Solve matrix equations

Q.13Inverse of a 3 x 3 matrix

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