F A- 2 -1 1- -1 2 -1- 1 -1 2 - verify that A3-6 A2-9 A-4 I-O and hence find A-1

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Byju's Answer

Standard XII

Mathematics

Derivative of One Function w.r.t Another

f A=[[ 2 -1 1...

Question

If verify that A³ − 6A² + 9A − 4I = O and hence find A⁻¹

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Solution

From equation (1), we have:

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Similar questions

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 & 1 - 1 & 2 & - 1 1 & - 1 & 2 \end{matrix} ⎤ ⎥ ⎦

, verify that

A^{3} - {6 A}^{2} + 9 A - 4 I = 0

. Hence find

A^{- 1}

Q. If

A = [\begin{matrix} 2 & - 1 & 1 \\ - 1 & 2 & - 1 \\ 1 & - 1 & 2 \end{matrix}]

. Verify that

A^{3} - 6 A^{2} + 9 A - 4 I = O

and hence find A⁻¹.

Q. If verify that A 3 − 6 A 2 + 9 A − 4 I = O and hence find A −1

If $A = ⎡ ⎢ ⎣ \begin{matrix} 2 & - 1 & 1 - 1 & 2 & - 1 1 & - 1 & 2 \end{matrix} ⎤ ⎥ ⎦$ verify that $A^{3} - 6 A^{2} + 9 A - 4 I = 0$ and hence, find $A^{- 1}$

Q. If

A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & - 3 2 & - 1 & 3 \end{matrix} ⎤ ⎥ ⎦

show that

A^{3} - 6 A^{2} + 5 A + 11 I = 0

. Hence find

A^{- 1}

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If verify that A3 − 6A2 + 9A − 4I = O and hence find A−1

From equation (1), we have:

If verify that A³ − 6A² + 9A − 4I = O and hence find A⁻¹