IXL - Properties of matrices (Algebra 1 practice)

–

and

–

is the following statement true or false?

true

false

ref_doc_title.

Learn with an example

question

–

and

–

is the following statement true or false?

true

false

key idea

A matrix product exists if and only if the number of columns in the first matrix equals the number of rows in the second matrix. If

has dimensions

and

has dimensions

then

has dimensions

(

)

(

)

Two matrices are equal if and only if their corresponding elements are equal.

solution

To see if the statement is true or false, find

and

Since

–

and

–

are square matrices with the same number of rows and columns, you can multiply them in either order.

and

will also be square matrices with 2 rows and 2 columns.

Since both matrix products exist, you can calculate them.

Calculate

Find the element in the

^st

row and

^st

column of

Multiply each element in the

^st

row of

by the corresponding element in the

^st

column of

Then, add the products.

–

(

)

(

–

)

(

–

)

Apply a similar process to find the element in the

^st

row and

^nd

column of

–

(

–

)

(

–

)

(

)

–

Repeat this process to calculate the remaining elements of

–

Calculate

Find the element in the

^st

row and

^st

column of

Multiply each element in the

^st

row of

by the corresponding element in the

^st

column of

Then, add the products.

–

(

)

(

–

)

(

–

)

Apply a similar process to find the element in the

^st

row and

^nd

column of

–

(

–

)

(

–

)

(

)

–

Repeat this process to calculate the remaining elements of

–

So,

–

and

–

Compare

and

Since

the statement is true.

However, this statement is not true for all matrices. In general, matrices do not satisfy the commutative property of multiplication. The statement

is true in this case only because of the particular values of

and

Looking for more? Try this:

$Confetti$

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Teacher tools

Work it out

Not feeling ready yet? These can help:

LL.6Multiply two matrices

LL.3Add and subtract matrices

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