If A = [(2,-3,5)(3,2,-4)(1,1,-2)]1. Find |A| 2. Find adj.A. 3. Solve 2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x + y – 2z = -3

Question

If A =\(\begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \)

1. Find |A|
2. Find adj.A. 
3. Solve 2x – 3y + 5z = 11, 3x + 2y – 4z = -5, x + y – 2z = -3

Answer 1

 1. If A = \(\begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \)

|A| = 2 × 0 + 3x – 2 + 5 = -1.

2. Co. factor A

\(\begin{bmatrix} 0 & 2 & 1 \\ -1 & -9 & -5 \\ 2 & 23 & 13 \end{bmatrix} \)

3. Given

i.e; AX = B ⇒ X = A^-1 B