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  • Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 11 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 4 Algebra of Matrices Exercise Very Short Asnwer Question 11 Maths Textbook Solution.

Answers (1)

best_answer

Answer: k=2

Hint: Here we use the concept of matrix scalar

Given:

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

A^{2}=kA

Solution:

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

A=\begin{bmatrix} 1 & -1\\ -1 &1 \end{bmatrix}\times \begin{bmatrix} 1 & -1\\ -1 &1 \end{bmatrix}

A=\begin{bmatrix} 1+1 & -1-1\\ -1-1 &1 +1\end{bmatrix}=\begin{bmatrix} 2 & -2\\ -2 &2 \end{bmatrix}

A^{2}=kA

\begin{bmatrix} 2 & -2\\ -2 &2 \end{bmatrix}=k\begin{bmatrix} 1 & -1\\ -1 & 1 \end{bmatrix}

2\begin{bmatrix} 1 & -1\\ -1 & 1 \end{bmatrix}=k\begin{bmatrix} 1 & -1\\ -1 & 1 \end{bmatrix}

k=2

 

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