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Matrices

Question

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Give example to show that .
AB = AC but B ≠ C.

Solution

Let space straight A equals space open square brackets table row 1 0 row 0 0 end table close square brackets space comma space straight B equals space open square brackets table row 0 0 row 2 0 end table close square brackets space comma straight C equals space open square brackets table row 0 0 row 0 3 end table close square brackets therefore space AB equals space open square brackets table row 1 0 row 0 0 end table close square brackets space open square brackets table row 0 0 row 0 2 end table close square brackets space equals space open square brackets table row cell 0 space plus end cell cell 0 space space space space 0 plus 0 end cell row cell 0 space plus end cell cell 0 space space space 0 plus 0 end cell end table close square brackets equals space open square brackets table row 0 0 row 0 0 end table close square brackets equals 0 space space space space space AC equals open square brackets table row 1 0 row 0 0 end table close square brackets space open square brackets table row 0 0 row 3 0 end table close square brackets space equals open square brackets table row cell 0 space plus end cell cell 0 space space space space 0 plus 0 end cell row cell 0 space plus end cell cell 0 space space space 0 plus 0 end cell end table close square brackets equals space open square brackets table row 0 0 row 0 0 end table close square brackets equals 0 therefore space AB equals AC space comma space but space space straight B space not equal to space straight C.

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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