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Find the adjoint and the inverse of the matrix A=1&2&\\3&-5\ |
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Answer» A= ⎝ ⎜ ⎜ ⎛
1 2
2 3 1
3 1 2
⎠ ⎟ ⎟ ⎞
∣A∣=1(6−1)−2(4−3)+3(2−6) 5−2−12 −9 Minor of A= ⎝ ⎜ ⎜ ⎛
5 1 −4
1 −4 −5
−4 −5 −1
⎠ ⎟ ⎟ ⎞
COF(A)= ⎝ ⎜ ⎜ ⎛
5 −1 −4
−1 −4 +5
−4 +5 −1
⎠ ⎟ ⎟ ⎞
ADJ (A)= ⎝ ⎜ ⎜ ⎛
5 −1 −4
−1 −1 5
−4 5 −1
⎠ ⎟ ⎟ ⎞
A −1 = ∣A∣ adj(A) = 9 1
⎝ ⎜ ⎜ ⎛
−5 1 4
1 4 −5
4 −5 1
⎠ ⎟ ⎟ ⎞
= 9 1
⎝ ⎜ ⎜ ⎛
−5 −1 4
1 4 −5
4 −5 1
⎠ ⎟ ⎟ ⎞
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