The matrix A - begin bmatrix -5 -8 - 0 3 - 5 - 0 11 - 2 -1lend bmatrix isA- orthogonalB- idempotentC- nilpotentD- involutory

The correct option is D involutoryA^2=[ 5 amp; 8 amp; 0; 3 amp; 5 amp; 0; 1 amp; 2 amp; 1 nbsp; nbsp; ][ 5 amp; 8 amp; 0; ...

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Standard XII

Mathematics

Elementary Transformations

The matrix A ...

Question

The matrix $A = ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦$ is

orthogonal

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idempotent

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involutory

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nilpotent

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Solution

The correct option is C involutory
$A^{2} = ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 0 & 1 & 0 0 & 0 & 1 \end{matrix} ⎤ ⎥ ⎦ = I$
Therefore, the given matrix $A$ is involutory.

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Similar questions

Show that

A = ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦

is involutory.

Q. matrix

A = ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦

Q. Compute the following:
(i)

[\begin{matrix} a & b - b & a \end{matrix}] + [\begin{matrix} a & b b & a \end{matrix}]

(ii)

[\begin{matrix} a^{2} + b^{2} & b^{2} + c^{2} a^{2} + c^{2} & a^{2} + b^{2} \end{matrix}] + [\begin{matrix} 2 a b & 2 b c - 2 a c & - 2 a b \end{matrix}]

(iii)

⎡ ⎢ ⎣ \begin{matrix} - 1 82 \end{matrix} \begin{matrix} 458 \end{matrix} \begin{matrix} - 6 165 \end{matrix} ⎤ ⎥ ⎦ + ⎡ ⎢ ⎣ \begin{matrix} 1283 \end{matrix} \begin{matrix} 702 \end{matrix} \begin{matrix} 654 \end{matrix} ⎤ ⎥ ⎦

(iv)

[\begin{matrix} {cos}^{2} x & {sin}^{2} x {sin}^{2} x & {cos}^{2} x \end{matrix}] + [\begin{matrix} {sin}^{2} x & {cos}^{2} x {cos}^{2} x & {sin}^{2} x \end{matrix}]

Q. If

[\begin{matrix} 2 & 1 3 & 2 \end{matrix}] A [\begin{matrix} - 3 & 2 5 & - 3 \end{matrix}] = [\begin{matrix} 1 & 0 0 & 1 \end{matrix}],

then the sum of all the elements of matrix

A

If $A = ⎡ ⎢ ⎣ \begin{matrix} - 1 & 2 & 3 5 & 7 & 9 - 2 & 1 & 1 \end{matrix} ⎤ ⎥ ⎦$ and $B = ⎡ ⎢ ⎣ \begin{matrix} - 4 & 1 & - 5 1 & 2 & 0 1 & 3 & 1 \end{matrix} ⎤ ⎥ ⎦$ , then verify that
(i)(A+B)'=A'+B'

(ii)(A-B)'=A'-B'

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The matrix A=⎡⎢⎣−5−8035012−1⎤⎥⎦ is

The correct option is C involutoryA2=⎡⎢⎣−5−8035012−1⎤⎥⎦⎡⎢⎣−5−8035012−1⎤⎥⎦=⎡⎢⎣100010001⎤⎥⎦=I Therefore, the given matrix A is involutory.

The matrix $A = ⎡ ⎢ ⎣ \begin{matrix} - 5 & - 8 & 0 3 & 5 & 0 1 & 2 & - 1 \end{matrix} ⎤ ⎥ ⎦$ is