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Matrices

Question
CBSEENMA12034184
Wired Faculty App

if space open square brackets table row 1 0 row 0 1 end table close square brackets comma space straight A equals open square brackets table row 0 1 row 0 0 end table close square brackets comma space then space show space that left parenthesis straight a space straight I space plus straight b space straight A right parenthesis cubed equals straight a cubed straight I plus 3 space straight a squared space bA.

Solution
Here space straight I space equals space open square brackets table row 1 0 row 0 1 end table close square brackets space space space space space space straight A equals space open square brackets table row 0 1 row 0 0 end table close square brackets therefore space straight a space straight I equals space open square brackets table row straight a 0 row 0 straight a end table close square brackets space comma space bA space equals space open square brackets table row 0 straight b row 0 straight a end table close square brackets therefore space straight a space straight I space plus straight b space straight A space equals space open square brackets table row straight a straight b row 0 straight a end table close square brackets therefore space left parenthesis straight a space straight I space plus space straight b space straight A right parenthesis squared equals space open square brackets table row straight a straight b row 0 straight a end table close square brackets space space open square brackets table row straight a straight b row 0 straight a end table close square brackets space equals space open square brackets table row cell straight a squared end cell cell 2 ab end cell row 0 cell straight a squared end cell end table close square brackets space space space space space space space left parenthesis straight a space straight I space plus space straight b space straight A right parenthesis cubed equals space open square brackets table row cell straight a squared end cell cell 2 ab end cell row 0 cell straight a squared end cell end table close square brackets space open square brackets table row straight a straight b row 0 straight a end table close square brackets space equals space open square brackets table row cell straight a cubed end cell cell 3 straight a squared straight b end cell row 0 cell straight a cubed end cell end table close square brackets therefore space space space left parenthesis straight a space straight I space plus space straight b space straight A right parenthesis cubed equals space space space open square brackets table row cell straight a cubed end cell cell 3 straight a squared straight b end cell row 0 cell straight a cubed end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space space space... left parenthesis 1 right parenthesis Also space space space space space straight a to the power of 3 space space end exponent straight I space plus 3 straight a squared space straight b space straight A space equals space straight a cubed space open square brackets table row 1 0 row 0 1 end table close square brackets plus 3 straight a squared space straight b space open square brackets table row 0 1 row 0 0 end table close square brackets space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space space equals open square brackets table row cell straight a cubed end cell cell 3 straight a to the power of 2 space end exponent straight b end cell row 0 cell straight a cubed end cell end table close square brackets space plus open square brackets table row 0 cell 3 straight a squared straight b end cell row 0 cell straight a cubed end cell end table close square brackets space space space space space space space space space space space space space space space space space space space space therefore space space space space space space space space straight a to the power of 3 space end exponent space straight I equals 3 straight a to the power of 2 space end exponent straight b space straight A equals space open square brackets table row cell straight a cubed end cell cell 3 straight a to the power of 2 space end exponent straight b end cell row 0 cell straight a cubed end cell end table close square brackets space space space space space space space space space From space left parenthesis 1 right parenthesis space space and space left parenthesis 2 right parenthesis. space we space get comma left parenthesis straight a space straight I space plus straight b space straight A space right parenthesis cubed space space space space space space space equals straight a cubed space space space straight I space plus 3 straight a squared space space bA.

Some More Questions From Matrices Chapter

If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements?

If a matrix A has 12 elements, what arc the possible orders it can have 7 What if it has 7 elements ?

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