Minors and Co-factors

If `"A" = [(1,1,1),(1,0,2),(3,1,1)]`, find A^-1. Hence, solve the system of equations x + y + z = 6, x + 2z = 7, 3x + y + z = 12.

Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}- 1 & 4 \\ 2 & 3\end{bmatrix}\]

If A `= [(0,1,1),(1,0,1),(1,1,0)] "then"  ("A"^2 - 3"I")/2 =` ____________.

Write \[A^{- 1}\text{ for }A = \begin{bmatrix}2 & 5 \\ 1 & 3\end{bmatrix}\]

Write the minor and cofactor of element of the first column of the following matrix and hence evaluate the determinant:

\[A = \begin{bmatrix}a & h & g \\ h & b & f \\ g & f & c\end{bmatrix}\]

If Δ = `|(a_11,a_12,a_13),(a_21,a_22,a_23),(a_31,a_32,a_33)|` and A_ij is Cofactors of a_ij, then the value of Δ is given by ______.

Write Minors and Cofactors of the elements of the following determinant:

`|(2,-4),(0,3)|`

`abs(("cos"  15°, "sin"  15°),("sin"  75°, "cos"  75°))`