Question

if A is matrix , then prove that A is a root of the polynomial f(x)=x^3-6x^2+7x+2​

Answer 1

$\textbf{Concept used:}$

$\text{A square matrix A is said to be}\;\textbf{Symmetric}\;\text{if}\;A=-A^{T}$

$\textbf{Given:}$

$A=\left(\begin{array}{ccc}0&a&-3\\2&0&-1\\b&1&0\end{array}\right)$

$\textbf{To find: a and b}$

$\text{Since A is skew symetric, we have}\;A=-A^{T}$

$\implies\,\left(\begin{array}{ccc}0&a&-3\\2&0&-1\\b&1&0\end{array}\right)=-\left(\begin{array}{ccc}0&2&b\\a&0&1\\-3&-1&0\end{array}\right)$

$\implies\,\left(\begin{array}{ccc}0&a&-3\\2&0&-1\\b&1&0\end{array}\right)=\left(\begin{array}{ccc}0&-2&-b\\-a&0&-1\\3&1&0\end{array}\right)$

$\text{Equating the corresponding elements, we get}$

$\textbf{a=2 and b=-3}$

$\therefore\textbf{The value of a is 2 and b is -3}$

Find more:

If A is square matrix, then which of the following is not true ? OPTIONS --- 1) AA' is symmetric 2) A-A' is skew symmetric. 3) A square is symmetric 4) A+A' is symmetric​

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