A=∣∣−6−1−6−4−45−46−1∣∣
Main determinant
∣A∣=−6∗((−4)∗(−1)−5∗6)−(−1)∗((−4)∗(−1)−5∗(−4))+−6∗((−4)∗6−(−4)∗(−4))=420
The determinant is non-zero, therefore, the matrix is non-degenerate and it is possible to find the inverse matrix A-1 for it.
The inverse matrix will look like this:
A−1=4201⎝⎛A11A21A31A12A22A32A13A23A33⎠⎞
where Aij are algebraic additions.
The transposed matrix.
A11=((−4)∗(−1)−6∗5)=−26A12=−((−4)∗(−1)−(−4)∗5)=−24A13=((−4)∗6−(−4)∗(−4))=−40A21=−((−1)∗(−1)−6∗(−6))=−37A22=((−6)∗(−1)−(−4)∗(−6))=−18A32=−((−6)∗6−(−4)∗(−1))=40A31=((−1)∗5−(−4)∗(−6))=−29A32=−((−6)∗5−(−4)∗(−6))=54A33=((−6)∗(−4)−(−4)∗(−1))=20
A−1=4201⎝⎛−26−37−29−24−1854−404020⎠⎞
A−1=⎝⎛210−13420−37420−2935−270−370921−2212211⎠⎞
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