Question

$Find space the space values space of space straight a space and space straight b space for space which space the space following space holds space colon open square brackets table row 4 2 row 3 cell negative 1 end cell end table close square brackets space open square brackets table row straight a row straight b end table close square brackets equals space open square brackets table row cell negative 4 end cell row 2 end table close square brackets$

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Solution

open square brackets table row 4 2 row 3 cell negative 1 end cell end table close square brackets space open square brackets table row straight a row straight b end table close square brackets equals space open square brackets table row cell negative 4 end cell row 2 end table close square brackets rightwards double arrow space open square brackets table row cell 4 straight a plus 2 straight b end cell row cell 3 straight a minus space straight b end cell end table close square brackets equals space open square brackets table row cell negative 4 end cell row 2 end table close square brackets By space definition space of space equality space of space matrices comma space space 4 straight a space plus space 2 straight b space equals space – space 4 space space space space... left parenthesis 1 right parenthesis space space 3 straight a space – space straight b space equals space 2 space space space space.... left parenthesis 2 right parenthesis space space Multiplying space left parenthesis 1 right parenthesis space by space 1 space and space left parenthesis 2 right parenthesis space by space 2 comma space we space get comma space space 4 straight a space plus space 2 straight b space equals space – space 4 space space space space... left parenthesis 3 right parenthesis space space 6 straight a space – space 2 straight b space equals space 4 space space space space... left parenthesis 4 right parenthesis space space Adding space left parenthesis 3 right parenthesis space and space left parenthesis 4 right parenthesis comma space we space get comma space space 1 Oa space equals space 0 space rightwards double arrow space straight a space equals space 0 space space therefore space from left parenthesis straight l right parenthesis comma space 0 space plus space 2 straight b space equals space – space 4 space rightwards double arrow space 2 straight b space equals space – space 4 space rightwards double arrow space straight b space equals space — space 2 space space therefore space we space have space straight a space equals space 0 comma space straight b space equals space — space 2.

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Matrices

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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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