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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 1 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Matrices Exercise 4.5 Question 1 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)

Find AT and prove that (A -A^{T}) = - (A - A^{T})

Given: A =\begin{bmatrix} 2 &3 \\ 4& 5 \end{bmatrix}

Solution:

 A^T= \begin{bmatrix} 2 & 4\\ 3 &5 \end{bmatrix}

A - A^{T} = \begin{bmatrix} 2 &3 \\ 4& 5 \end{bmatrix}-\begin{bmatrix} 2 &4 \\ 3& 5 \end{bmatrix}

= \begin{bmatrix} 0 &-1 \\ 1& 0 \end{bmatrix}

= B

B^{T} = \begin{bmatrix} 0 &1 \\ -1 &0 \end{bmatrix}

-B^{T} = \begin{bmatrix} 0 &-1 \\ 1 &0 \end{bmatrix}

- B^{T}= B

Hence,

B is a skew-symmetric matrix.

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