First slide

Introduction to matrices

Question

$If A = [\begin{array}{ccc} 0 & 1 & 0 \\ 0 & 0 & 1 \\ - c & - b & - a \end{array}] then A^{3} + a A^{2} + b A + c I is$

Moderate

A

real number zero
B

$2 \times 2$ null matrix
C

a $3 \times 3$ null matrix
D

none

Solution

Since $A i s 3 \times 3$ matrix
$A^{3} + a A^{2} + b A + c I$ is also a $3 \times 3$ matrix

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