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Matrices

Short Answer Type

41. Compute the following :

open square brackets table row cell negative 1 end cell 4 cell negative 6 end cell row 8 5 16 row 2 8 5 end table close square brackets plus open square brackets table row 12 7 6 row 8 0 5 row 3 2 4 end table close square brackets

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42. Compute the following :

open square brackets table row cell cos squared straight x end cell cell sin squared straight x end cell row cell sin squared straight x end cell cell cos squared straight x end cell end table close square brackets plus open square brackets table row cell sin squared x end cell cell cos squared x end cell row cell cos squared x end cell cell sin squared x end cell end table close square brackets

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43.

If $straight A equals open square brackets table row 1 4 cell negative 1 end cell row 2 6 5 end table close square brackets space and space straight B equals open square brackets table row 3 cell negative 2 end cell cell negative 6 end cell row 2 0 cell negative 7 end cell end table close square brackets$ , find A + B and A - B.

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44.
If $straight A equals open square brackets table row 1 2 cell negative 3 end cell row 5 0 2 row 1 cell negative 1 end cell 1 end table close square brackets comma space straight B equals open square brackets table row 3 cell negative 1 end cell 2 row 4 2 5 row 2 0 3 end table close square brackets space and space straight C equals open square brackets table row 4 1 2 row 0 3 3 row 1 cell negative 2 end cell 3 end table close square brackets.$ compute (A + B) and (B – C). Also verify that A+ (B – C) = (A + B) – C.

straight A equals open square brackets table row 1 2 cell negative 3 end cell row 5 0 2 row 1 cell negative 1 end cell 1 end table close square brackets comma space straight B equals open square brackets table row 3 cell asterisk times 1 end cell 2 row 4 2 5 row 2 0 3 end table close square brackets comma space straight C equals open square brackets table row 4 1 2 row 0 3 2 row 1 cell negative 2 end cell 3 end table close square brackets straight A plus straight B equals open square brackets table row 1 2 cell negative 3 end cell row 5 0 2 row 1 cell negative 1 end cell 1 end table close square brackets plus open square brackets table row 3 cell negative 1 end cell 2 row 4 2 5 row 2 0 3 end table close square brackets space space space space space space space space space space space equals open square brackets table row cell 1 plus 3 end cell cell 2 minus 1 end cell cell negative 3 plus 2 end cell row cell 5 plus 4 end cell cell 0 plus 2 end cell cell 2 plus 5 end cell row cell 1 plus 2 end cell cell negative 1 plus 0 end cell cell 1 plus 3 end cell end table close square brackets equals open square brackets table row 4 1 cell negative 1 end cell row 9 2 7 row 3 cell negative 1 end cell 4 end table close square brackets straight B minus straight C equals open square brackets table row 3 cell negative 1 end cell 2 row 4 2 5 row 2 0 3 end table close square brackets minus open square brackets table row 4 1 2 row 0 3 2 row 1 cell negative 2 end cell 3 end table close square brackets space space space space space space space space space space open square brackets table row cell 3 minus 4 end cell cell negative 1 minus 1 end cell cell 2 minus 2 end cell row cell 4 minus 0 end cell cell 2 minus 3 end cell cell 5 minus 2 end cell row cell 2 minus 1 end cell cell 0 plus 2 end cell cell 3 minus 3 end cell end table close square brackets equals open square brackets table row cell negative 1 end cell cell negative 2 end cell 0 row 4 cell negative 1 end cell 3 row 1 2 0 end table close square brackets Now space space space space space straight A plus left parenthesis straight B minus straight C right parenthesis equals open square brackets table row 1 2 cell negative 3 end cell row 5 0 2 row 1 cell negative 1 end cell 1 end table close square brackets plus open square brackets table row cell negative 1 end cell cell negative 2 end cell 0 row 4 cell negative 1 end cell 3 row 1 2 0 end table close square brackets 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 1 minus 1 end cell cell 2 minus 2 end cell cell negative 3 plus 0 end cell row cell 5 plus 4 end cell cell 0 minus 1 end cell cell 2 plus 3 end cell row cell 1 plus 1 end cell cell negative 1 plus 2 end cell cell 1 plus 0 end cell end table close square brackets therefore space space space space space straight A plus left parenthesis straight B minus straight C right parenthesis space equals space open square brackets table row 0 0 cell negative 3 end cell row 9 cell negative 1 end cell 5 row 2 1 1 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... left parenthesis 1 right parenthesis space space space space space space space left parenthesis straight A plus straight B right parenthesis minus straight C equals open square brackets table row 4 1 cell negative 1 end cell row 9 2 7 row 3 cell negative 1 end cell 4 end table close square brackets minus open square brackets table row 4 1 2 row 0 3 2 row 1 cell negative 2 end cell 3 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 equals space open square brackets table row cell 4 minus 4 end cell cell 1 minus 1 end cell cell negative 1 minus 2 end cell row cell 9 minus 0 end cell cell 2 minus 3 end cell cell 7 minus 2 end cell row cell 3 minus 1 end cell cell negative 1 plus 2 end cell cell 4 minus 3 end cell end table close square brackets therefore space space space left parenthesis straight A plus straight B right parenthesis minus straight C equals open square brackets table row 0 0 cell negative 3 end cell row 9 cell negative 1 end cell 5 row 2 1 1 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

From (1) and (2), A + (B - C) = (A + B)-C

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45. If

straight A equals open square brackets table row 1 2 3 row 2 3 1 end table close square brackets space and space straight B equals open square brackets table row 3 cell negative 1 end cell 3 row cell negative 1 end cell 0 2 end table close square brackets

, then find 2A - B.

88 Views

Long Answer Type

46.

$If space space straight A equals open square brackets table row cell 2 over 3 end cell 1 cell 5 over 3 end cell row cell 1 third end cell cell 2 over 3 end cell cell 4 over 3 end cell row cell 7 over 3 end cell 2 cell 2 over 3 end cell end table close square brackets space and space straight B space equals open square brackets table row cell 2 over 5 end cell cell 3 over 5 end cell 1 row cell 1 fifth end cell cell 2 over 5 end cell cell 4 over 5 end cell row cell 7 over 5 end cell cell 6 over 5 end cell cell 2 over 5 end cell end table close square brackets$ then computer 3A-5B