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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 2 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 2 Maths.

Answers (1)

Answer:A - A^{T} is a skew-symmetric matrix.

Hint: MatrixB is said to be skew-symmetric if transpose of matrix A is equal to negative of matrix A i.e (B^{T} = -B)

Prove that : (A - A^{T}) = - (A - A^{T})

Given:

A=\begin{bmatrix} 3 &-4 \\ 1 & 1 \end{bmatrix}

Solution:

A^{T}=\begin{bmatrix} 3 &1 \\ -4 & 1 \end{bmatrix}

A - A^{T} =\begin{bmatrix} 3 &-4 \\ 1& 1 \end{bmatrix} - \begin{bmatrix} 3& 1\\ -4 &1 \end{bmatrix}

=\begin{bmatrix} 0 & -5\\ 5& 0 \end{bmatrix}

= B

B^{T} =\begin{bmatrix} 0 &5 \\ -5& 0 \end{bmatrix}

-B^{T} =\begin{bmatrix} 0 &-5 \\ 5& 0 \end{bmatrix}

- B^{T} = B

Hence,

B is a skew-symmetric matrix.

 

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infoexpert27

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