If matrix A - -aij-3-3- matrix B - -bij-3-3 where aij - aji - 0 and bij - bji-0-then -A4-B3- is

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Standard XIII

Mathematics

Singular and Non Singualar Matrices

If matrix A =...

Question

$I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n | A^{4} . B^{3} | i s$

skew-symmetric matrix

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singular

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symmetric

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zero matrix

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Solution

The correct option is B
singular

Since matrix A is skew-symmetric,
$∴ | A | = 0$
$∴ | A^{4} . B^{3} | = 0$

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Similar questions

$I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n | A^{4} . B^{3} | i s$

I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n A^{4} . B^{3} i s

Q. Let

P = [a_{i j}]

be a 3

\times

3 matrix and let

Q = [b_{i j}]

, where

b_{i j} = 2^{i + j} a_{i j}

for

1 \leq i, j \leq 3

. If the determinant of P is 2, then the determinant of the matrix Q is

Q. Let

P = [a_{i j}]

be a

3 \times 3

matrix and let

Q = (b_{i j})

where

b_{i j} = 2^{i + j} a_{i j}

for

1 \leq i, j \leq 3

. If the determinant of P is

2

then the determinant of the matrix Q is?

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If matrix A=[aij]3×3,matrix B=[bij]3×3 where aij+aji=0 and bij−bji=0,then |A4.B3| is

The correct option is B singular Since matrix A is skew-symmetric, ∴|A|=0 ∴|A4.B3|=0

$I f m a t r i x A = [a_{i j}]_{3 \times 3}, m a t r i x B = [b_{i j}]_{3 \times 3} w h e r e a_{i j} + a_{j i} = 0 a n d b_{i j} - b_{j i} = 0, t h e n | A^{4} . B^{3} | i s$

The correct option is B
singular

Since matrix A is skew-symmetric,
$∴ | A | = 0$
$∴ | A^{4} . B^{3} | = 0$