Question
If A =
, then A2 equals-
The correct answer is: ![open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets](data:image/png;base64,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)
To find the value of
for the given matrix A.
Given A =
.
=
x ![open square brackets table row cell cos invisible function application alpha end cell cell sin invisible function application alpha end cell row cell negative sin invisible function application alpha end cell cell cos invisible function application alpha end cell end table close square brackets](data:image/png;base64,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)
=![open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets](data:image/png;base64,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)
Therefore, using matrix multiplication,
= =![open square brackets table row cell cos invisible function application 2 alpha end cell cell sin invisible function application 2 alpha end cell row cell negative sin invisible function application 2 alpha end cell cell cos invisible function application 2 alpha end cell end table close square brackets](data:image/png;base64,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)
Related Questions to study
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Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.
Statement - II The maximum value of sin x + cos x occurs when x =
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.
Statement - I The value of x for which (sin x + cos x)1 + sin 2x = 2, when 0 ≤ x ≤ , is only.
Statement - II The maximum value of sin x + cos x occurs when x =
In this question, we have to find the statements are the correct or not and statement 2 is correct explanation or not, is same as assertion and reason.