In this page inverse of matrix questions 5 we are going to see solution of question 5 in the topic inverse of matrix.
Question 5
Find the inverse of the following matrix
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Solution:
|A| |
= 3 |
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- 1 |
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-1 |
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|A| = 3 [2-2] - 1 [-4-4] - 1 [2-(-2)]
= 3 [0] - 1 [-8] -1 [2+2]
= 3 [0] - 1 [-8] -1 [4]
= 0 + 8 - 4
= 4
|A| = 4 ≠ 0
Since A is a non singular matrix. A⁻¹ exists.
minor of 4 |
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= [2-2] = 0 | ||||||||||
Cofactor of 4 |
= + (0) = 0 | |||||||||
minor of 1 |
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= [-4-4] = (-8) = -8 | ||||||||||
Cofactor of 1 |
= - (-8) = 8 | |||||||||
minor of -1 |
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inverse of matrix questions 5 inverse of matrix questions 5 |
= [2-(-2)] = (2+2) = 4 | |||||||||
Cofactor of -1 |
= + (4) = 4 | |||||||||
minor of 2 |
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= [-2-(-1)] = (-2+1) = -1 = -1 | ||||||||||
Cofactor of 2 |
= - (-1) = 1 | |||||||||
minor of -1 |
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= [-6-(-2)] = (-6+2) = -4 = -4 | ||||||||||
Cofactor of -1 |
= + (-4) = -4 | |||||||||
minor of 2 |
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= [3-2] = 1 | ||||||||||
Cofactor of 2 |
= - (1) = -1 | |||||||||
minor of 2 |
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= [2-1] = 1 | ||||||||||
Cofactor of 2 |
= + (1) = 1 | |||||||||
minor of 1 |
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= [6-(-2)] = [6+2] = 8 | ||||||||||
Cofactor of 1 |
= - (8) = -8 | |||||||||
minor of -2 |
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= [-3-2] = [-5] = -5 | ||||||||||
Cofactor of -2 |
= + (-5) = -5 |
co-factor matrix = |
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adjoint of matrix= |
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A⁻¹ = 1/4 |
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Questions |
Solution | |||||||||||||
1) Find the inverse of the following matrix |
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2) Find the inverse of the following matrix |
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3) Find the inverse of the following matrix |
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4) Find the inverse of the following matrix |
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