For the matrix A- 1 1 1- 1 2 -3- 2 -1 3 - show that A3-6 A2-5 A-11 I-0- Hence- find A-3

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Standard XII

Mathematics

Integration by Partial Fractions

For the matri...

Question

For the matrixshow that A³ − 6A² + 5A + 11 I = O. Hence, find A^−1.

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Solution

From equation (1), we have:

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Similar questions

Q. For the matrix

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}

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}

Q. For the matrix show that A 3 − 6 A 2 + 5 A + 11 I = O. Hence, find A −1.

For the matrix $A = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 1 & 2 & - 3 2 & - 1 & 3 \end{matrix} ⎤ ⎥ ⎦$ . Show that $A^{3} - 6 A^{2} + 5 A + 11 I = 0$ . Hence, find $A^{- 1}$

Q. For the matrix

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_{3} = O

. Hence, find A⁻¹.

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For the matrixshow that A3 − 6A2 + 5A + 11 I = O. Hence, find A−1.

From equation (1), we have:

For the matrixshow that A³ − 6A² + 5A + 11 I = O. Hence, find A^−1.