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CBSE XII
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For the matrix \( A= \begin{bmatrix} 1 & 1 & 1 \\ 1 & 2 & -3 \\ 2 & -1 & 3 \end{bmatrix} \), show that \( A^3-6A^2+5A+11I=0.\) Hence, find \(A^{-1}.\)
This question has appeared in textbook.
cbse
class12
modelpaper
2012
sec-c
q23
ch4
bookproblem
sec5
q15
p132
math
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asked
Jan 27, 2013
by
thanvigandhi_1
edited
Apr 9, 2013
by
sreemathi.v
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Related questions
\[ \text{For the matrix A = } \begin{bmatrix} 1&1&1 \\ 1& 2&- 3 \\ 2 &-1& 3 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 5A + 11I = O. \text{ Hence, find } A^{-1}\]
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\[ \text{For the matrix A = } \begin{bmatrix} 2&-1&1 \\ -1& 2&- 1 \\ 1 &-1& 2 \end{bmatrix} \] \[ \text{Show that } A^{3} - 6A^{2} + 9A - 4I = O. \text{ Hence, find } A^{-1}\]
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Feb 26, 2013
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\[ \text{If A = } \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}, \text{show that } A^{2} -5A +7I = 0. \text{ Hence find } A^{-1}\]
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\[ \text{Let A = } \begin{bmatrix} 3 & 7 \\ 2 & 5 \end{bmatrix} \text{and B = } \begin{bmatrix} 6 & 8 \\ 7 & 9 \end{bmatrix}. \text{Verify that } (AB^{-1}) = B^{-1}A^{-1}\]
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\[ \text{For the matrix A = } \begin{bmatrix} 3 & 2 \\ 1 & 1 \end{bmatrix}, \text{ find the numbers a and b such that } A^{2} + aA + bI = O \]
cbse
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If $A = \begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} $ find \( A^{-1}\). Using \( A^{-1}\) solve the system of equations:\( 2x-3y+5z=11; 3x+2y-4z=-5; x+y-2z = -3\)
cbse
class12
modelpaper
2012
sec-c
q23
ch4
bookproblem
sec6
q15
p137
math
asked
Feb 7, 2013
by
thanvigandhi_1
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answers
Find the inverse of the matrix (if it exists): \[ \begin{bmatrix} 1 & -1 & 2 \\ 0 & 2 & -3 \\ 3 & -2 & 4 \\ \end{bmatrix} \]
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Nov 29, 2012
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balaji.thirumalai
1
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