First slide

Operations of matrix

Question

if $A = [\begin{array}{cccc} x - 1 & 0 & 2 & 5 \\ 3 & x^{2} - 2 & 4 & 1 \\ - 1 & - 2 & x - 3 & 1 \\ 2 & 0 & 4 & x^{2} - 6 \end{array}]$ and if Tr(A) = 0, then sum of the values of x is equal to

Moderate

Solution

Trace of the matrix is defined as
$\begin{array}{l} \sum_{i = 1}^{n} a_{ii} = 2 x^{2} + 2 x - 12 = 0 \\ \Rightarrow x = - 3, 2 \end{array}$

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