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  • Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 42

Provide solution for RD Sharma maths class 12 chapter 4 Algebra of Matrices exercise Fill in the blank question 42

Answers (1)

Answer:

 0

Hint:

 For this we must aware with skew symmetric matrix

Given:

 A=\left[\begin{array}{ccc} 0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0 \end{array}\right] \text { is skew symmetric }

Solution:

\begin{aligned} &A^{T}=-A \\ &{\left[\begin{array}{ccc} 0 & -1 & -1 \\ a & b & c \\ 1 & 1 & 0 \end{array}\right]=-1\left[\begin{array}{ccc} 0 & a & 1 \\ -1 & b & 1 \\ -1 & c & 0 \end{array}\right]} \\ &{\left[\begin{array}{ccc} 0 & -1 & -1 \\ a & b & c \\ 1 & 1 & 0 \end{array}\right]=\left[\begin{array}{ccc} 0 & -a & -1 \\ 1 & -b & -1 \\ 1 & -c & 0 \end{array}\right]} \end{aligned}

So both sides have 3 x 3 matrix

So,

\begin{aligned} &a=1 \\ &b=-b \\ &b+b=0 \\ &2 b=0 \\ &c=-1 \\ &\text { So, }(a+b+c)^{2}=(-1+0+(-1))^{2}=(0)^{2}=0 \end{aligned}

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