If A is a symmetric matrix and B is skew- symmetric matrix such that A + B = 2 3 5 - 1 , then A B is equal to:

Given A is symmetric and B is skew symmetric, hence A = a b b c and B = 0 d - d 0 Now A + B = a b + d b - d c = 2 3 5 - 1 ⇒ a = 2 , b = 4 , c = - 1 and d = - 1 ⇒ A = 2 4 4 - 1 and B = 0 - 1 1 0 Hence A B = 2 4 4 - 1 0 - 1 1 0 = 4 - 2 - 1 - 4

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MathematicsMatricesSymmetric & Skew Symmetric MatricesEasy2 minPYQ_2019

MathematicsEasysingle choice

If $A$ is a symmetric matrix and $B$ is skew- symmetric matrix such that $A + B = [\begin{matrix} 2 & 3 \\ 5 & - 1 \end{matrix}]$ , then $A B$ is equal to:

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Answer:

Solution:

Given $A$ is symmetric and $B$ is skew symmetric, hence
$A = [\begin{matrix} a & b \\ b & c \end{matrix}]$ and $B = [\begin{matrix} 0 & d \\ - d & 0 \end{matrix}]$
Now $A + B = [\begin{matrix} a & b + d \\ b - d & c \end{matrix}] = [\begin{matrix} 2 & 3 \\ 5 & - 1 \end{matrix}]$
$\Rightarrow a = 2, b = 4, c = - 1$ and $d = - 1$
$\Rightarrow A = [\begin{matrix} 2 & 4 \\ 4 & - 1 \end{matrix}]$ and $B = [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]$
Hence $A B = [\begin{matrix} 2 & 4 \\ 4 & - 1 \end{matrix}] [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 4 & - 2 \\ - 1 & - 4 \end{matrix}]$

Stream:JEESubject:MathematicsTopic:MatricesSubtopic:Symmetric & Skew Symmetric Matrices

⏱ 2mℹ️ Source: PYQ_2019

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