topic badge

4.06 Powers of matrices

Interactive practice questions

Consider the matrix $A$A, defined below.

Which option correctly describes the result of the calculation $A^2$A2?

$A$A=
    $-6$6 $-2$2 $2$2    
    $3$3 $-2$2 $4$4    
     

$A^2$A2 cannot be found. It would require multiplying a $2\times3$2×3 matrix by a $2\times3$2×3 matrix, and the sizes of these matrices do not match for the purpose of matrix multiplication.

A

$A^2$A2 can be found by squaring every element of $A$A. The resulting matrix will be

$A^2$A2=
    $36$36 $4$4 $4$4    
    $9$9 $4$4 $16$16    
     
B

$A^2$A2 can be found by the following process. First turn $A$A into a square matrix by removing the last column, then multiply the new matrix by itself. The result will be

$A^2$A2=
    $30$30 $16$16    
    $-24$24 $-2$2    
     
C

$A^2$A2 cannot be found, since you can only square $1\times1$1×1, $2\times2$2×2 and $3\times3$3×3 matrices and $A$A is not any of these sizes.

D
Easy
< 1min

Consider the matrix $A$A, defined below.

Which option correctly states whether $A^2$A2 can be found and why?

Easy
< 1min

Can the following matrix be squared?

Easy
< 1min

Can the following matrix be squared?

Easy
< 1min
Sign up to access Practice Questions
Get full access to our content with a Mathspace account

Outcomes

ACMGM016

use matrices, including matrix products and powers of matrices, to model and solve problems; for example, costing or pricing problems, squaring a matrix to determine the number of ways pairs of people in a communication network can communicate with each other via a third person

What is Mathspace

About Mathspace