Express the matrix A = \left(\begin{array}{ccc}4 & 2 & −3 \ \\\\text{ }\\\1 & 3 & −6 \ \\\\text{ }\\\−5 & 0 & −7 \ )\end{array} as the sum of a symmetric and a skew-symmetric matrix.

Correct Answer is : (41.5−4 1.53−3 −4−3−7)+(00.51 −0.50−3 −130)

\left(\begin{array}{ccc}4 & 1.5 & −4 \ \\\\text{ }\\\1.5 & 3 & −3 \ \\\\text{ }\\\−4 & −3 & −7 \ )\end{array} + \left(\begin{array}{ccc}2 & 0.5 & 1 \ \\\\text{ }\\\−0.5 & 0 & −3 \ \\\\text{ }\\\−1 & 3 & 0 \ )\end{array}

\left(\begin{array}{ccc}4 & 1.5 & −4 \ \\\\text{ }\\\1.5 & 1 & −3 \ \\\\text{ }\\\−4 & −3 & −7 \ )\end{array} + \left(\begin{array}{ccc}0 & 0.5 & 1 \ \\\\text{ }\\\−0.5 & 0 & −3 \ \\\\text{ }\\\−1 & 3 & 0 \ )\end{array}

\left(\begin{array}{ccc}4 & 1.5 & −4 \ \\\\text{ }\\\1.5 & 3 & −3 \ \\\\text{ }\\\−4 & −3 & −7 \ )\end{array} + \left(\begin{array}{ccc}0 & 0.5 & 1 \ \\\\text{ }\\\−0.5 & 2 & −3 \ \\\\text{ }\\\−1 & 3 & 0 \ )\end{array}

\left(\begin{array}{ccc}4 & 1.5 & −4 \ \\\\text{ }\\\1.5 & 3 & −3 \ \\\\text{ }\\\−4 & −3 & −7 \ )\end{array} + \left(\begin{array}{ccc}0 & 0.5 & 1 \ \\\\text{ }\\\−0.5 & 0 & −3 \ \\\\text{ }\\\−1 & 3 & 0 \ )\end{array}

AAI ATC Junior Executive 27 Jul 2022 Shift 3 Paper

Question : 89 of 120

Marks: +1, -0

Express the matrix

A = {(\table 4 , 2 , −3 ; \;\text " "\;1 , 3 , −6 ; \;\text " "\;−5 , 0 , −7 ; )}

as the sum of a symmetric and a skew-symmetric matrix.

${(\table 4 , 1.5 , −4 ; \;\text " "\;1.5 , 3 , −3 ; \;\text " "\;−4 , −3 , −7 ; )} + {(\table 2 , 0.5 , 1 ; \;\text " "\;−0.5 , 0 , −3 ; \;\text " "\;−1 , 3 , 0 ; )}$
${(\table 4 , 1.5 , −4 ; \;\text " "\;1.5 , 1 , −3 ; \;\text " "\;−4 , −3 , −7 ; )} + {(\table 0 , 0.5 , 1 ; \;\text " "\;−0.5 , 0 , −3 ; \;\text " "\;−1 , 3 , 0 ; )}$
${(\table 4 , 1.5 , −4 ; \;\text " "\;1.5 , 3 , −3 ; \;\text " "\;−4 , −3 , −7 ; )} + {(\table 0 , 0.5 , 1 ; \;\text " "\;−0.5 , 2 , −3 ; \;\text " "\;−1 , 3 , 0 ; )}$
${(\table 4 , 1.5 , −4 ; \;\text " "\;1.5 , 3 , −3 ; \;\text " "\;−4 , −3 , −7 ; )} + {(\table 0 , 0.5 , 1 ; \;\text " "\;−0.5 , 0 , −3 ; \;\text " "\;−1 , 3 , 0 ; )}$

Validate

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