Question
List the diagonal entries of $A=\left(\begin{array}{rrrr}1 & 2 & 3 & 4 \\ 5 & 6 & 7 & 8 \\ 9 & 10 & 11 & 12 \\ 13 & 14 & 15 & 16\end{array}\right)$.
Step 1
The diagonal entries of a matrix are those entries that are located from the top left corner to the bottom right corner of the matrix. These entries have the same row and column index. Show more…
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Find the diagonal and trace of each matrix: (a) $A=\left[\begin{array}{rrr}1 & 3 & 6 \\ 2 & -5 & 8 \\ 4 & -2 & 9\end{array}\right]$ (b) $B=\left[\begin{array}{rrr}2 & 4 & 8 \\ 3 & -7 & 9 \\ -5 & 0 & 2\end{array}\right]$ (c) $\quad C=\left[\begin{array}{rrr}1 & 2 & -3 \\ 4 & -5 & 6\end{array}\right]$.
Find the transpose of each matrix. $$ \left[\begin{array}{ccc}{1} & {11} & {15} \\ {0} & {10} & {-6} \\ {4} & {12} & {-2} \\ {1} & {-1} & {13} \\ {2} & {25} & {-1}\end{array}\right] $$
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4. a. Find the diagonal entries of AB by inspection. A = [4 0 0; -2 0 0; -3 0 7], B = [6 0 0; 1 5 0; 3 2 6] b. Find a diagonal matrix A, given A^-2 = [9 0 0; 0 4 0; 0 0 1]
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