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Let A be a 3*3 matrix whose characteristics roots are 3,2,1. If $B=A^2A$ then B=?
a)24
b)2
c)12
d)12
Please explain in detail.
linearalgebra
matrix
eigenvalue
asked
Jan 19
in
Linear Algebra
by
Reshu $ingh
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Best answer
Let
A = $\begin{bmatrix} 3 &0 &0 \\ 0&2 &0 \\ 0&0 &1 \end{bmatrix}$
A$^{2}$ = $\begin{bmatrix} 9 &0 &0 \\ 0&4 &0 \\ 0&0 &1 \end{bmatrix}$
B = A$^{2}$  A
=$\begin{bmatrix} 6 &0 &0 \\ 0&2 &0 \\ 0&0 &2 \end{bmatrix}$
Thus B = 24
answered
Jan 20
by
Rishabh Agrawal
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Jan 20
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Reshu $ingh
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