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6. Matrices
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AustraliaVIC
VCE 11 General 2023

6.08 Inverse matrices

Lesson
Worksheet
Practice

Interactive practice questions

The following matrices are inverses. What is their product (in either order)?

 
    $2$2 $3$3 $7$7    
    $6$6 $0$0 $5$5    
    $1$1 $4$4 $8$8    
and
    $20$20 $-4$−4 $-15$−15    
    $43$43 $-9$−9 $-32$−32    
    $-24$−24 $5$5 $18$18    
 
    $\editable{}$ $\editable{}$ $\editable{}$    
    $\editable{}$ $\editable{}$ $\editable{}$    
    $\editable{}$ $\editable{}$ $\editable{}$    
Hard
1min

Is $I_3A$I3​A equal to $A$A?

Find out by multiplying the following matrices.

$A$A$=$=
    $5$5 $-3$−3 $8$8    
    $7$7 $-6$−6 $2$2    
    $4$4 $0$0 $0$0    
and $I_3$I3​$=$=
    $1$1 $0$0 $0$0    
    $0$0 $1$1 $0$0    
    $0$0 $0$0 $1$1    
 
Hard
1min
Consider the matrices $A$A$=$=
    $1$1 $1$1 $2$2    
    $1$1 $0$0 $0$0    
    $0$0 $0$0 $0$0    
and $B$B$=$=
    $0$0 $1$1 $0$0    
    $1$1 $-1$−1 $-2$−2    
    $0$0 $0$0 $1$1    

We want to determine whether $A$A and $B$B are inverses of each other.

Hard
1min
Evaluate the determinant    $\frac{1}{3}$13​ $-15$−15   .
  $\frac{4}{5}$45​ $-6$−6  
Easy
< 1min
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Outcomes

U1.AoS3.4

determinant and inverse of a matrix

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