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The matrix [{:(0,-5,8),(5,0,12),(-8,-12,...

The matrix `[{:(0,-5,8),(5,0,12),(-8,-12,0):}]` is a

A

diagonal matrix

B

symmetric matrix

C

skew-symmetric matrix

D

scalar matrix.

Text Solution

Verified by Experts

The correct Answer is:
C
We know that in a square matrix if `b_(ij)=0`, when `inej`. Then it is said to be a diagonal matrix, Here `b_(12).b_(13)........ne0`, so the given matrix is not a diagonal matrix,
Now, `B=[{:(0,-5,8),(5,0,12),(-8,-12,0):}] `
`therefore B'=[{:(0,5,-8),(-5,0,-12),(8,12,0):}]=-[{:(0, -5, 8),( 5,0,12),(-8,-12,0):}]=-B`
So, the given matrix is a skew-symmetric since we know tha in a square matrix B, if `B'=-B`, then it is called skew-symmetric matrix.
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