If A = diag[2, – 3, – 5], B = diag[4, – 6, – 3] and C = diag[– 3, 4, 1] then find 2A + B

Engineering

Mathematics

Multiplication of Matrices

Symmetric and Skew Symmetric Matrices

Question

If A = diag[2, – 3, – 5], B = diag[4, – 6, – 3] and C = diag[– 3, 4, 1] then find 2A + B – 5C

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$A = [\begin{array}{ccc} 2 & 0 & 0 \\ 0 & - 3 & 0 \\ 0 & 0 & - 5 \end{array}] B = [\begin{array}{ccc} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & - 3 \end{array}] C = [\begin{array}{ccc} - 3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{array}]$

$2 A + B - 5 C = 2 [\begin{array}{ccc} 2 & 0 & 0 \\ 0 & - 3 & 0 \\ 0 & 0 & - 5 \end{array}] + [\begin{array}{ccc} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & - 3 \end{array}] - 5 [\begin{array}{ccc} - 3 & 0 & 0 \\ 0 & 4 & 0 \\ 0 & 0 & 1 \end{array}]$

$2 A + B - 5 C = [\begin{array}{ccc} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & - 10 \end{array}] + [\begin{array}{ccc} 4 & 0 & 0 \\ 0 & - 6 & 0 \\ 0 & 0 & - 3 \end{array}] - [\begin{array}{ccc} - 15 & 0 & 0 \\ 0 & 20 & 0 \\ 0 & 0 & 5 \end{array}]$

$2 A + B - 5 C = [\begin{array}{ccc} 8 & 0 & 0 \\ 0 & - 12 & 0 \\ 0 & 0 & - 13 \end{array}] - [\begin{array}{ccc} - 15 & 0 & 0 \\ 0 & 20 & 0 \\ 0 & 0 & 5 \end{array}]$

$2 A + B - 5 C = [\begin{array}{ccc} 23 & 0 & 0 \\ 0 & - 32 & 0 \\ 0 & 0 & - 18 \end{array}]$

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