Math, asked by satyamjakhmola99, 11 months ago

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

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Answered by MaheswariS
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\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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