Honors: 8.05 Applications of inverses and determinants
Adaptive
Worksheet
Interactive practice questions
$A$A, $B$B and $C$C are matrices such that $AB=C$AB=C. Using matrix algebra, fill in the gaps to solve for matrix $B$B.
| Multiply both sides of the equation by the inverse of $\editable{}$: | $\left(\editable{}\right)^{-1}\editable{}B=\left(\editable{}\right)^{-1}C$()−1B=()−1C |
| The product of any matrix and its inverse results in the identity matrix: | $\editable{}B=\left(\editable{}\right)^{-1}C$B=()−1C |
| The product of any matrix and the identity matrix is the matrix itself: | $\editable{}=\left(\editable{}\right)^{-1}C$=()−1C |
Easy
2min
$A$A, $B$B and $C$C are matrices such that $AB+C=0$AB+C=0. Using matrix algebra, fill in the gaps to solve for matrix $B$B.
Easy
1min
| Let $A$A$=$= |
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, and $P$P$=$= |
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Find $X$X, if $AX=P$AX=P, in its most simplified form.
Medium
4min
| Consider the matrix $P$P$=$= |
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Find a solution of $X$X to the equation $PX=P$PX=P.
Medium
< 1min
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