Let P = \begin{bmatrix}a & b & 0\\\\-1 & 2 & 1\\\2 & -3 & -2 \end{bmatrix} with det(P) = -2. Then the minor M_{22} of P is

Question 40

Let

$$P = \begin{bmatrix}a & b & 0\\-1 & 2 & 1\\2 & -3 & -2 \end{bmatrix}$$

with $$det(P) = -2$$. Then the minor $$M_{22}$$ of $$P$$ is

Solution

$$det(P)$$ = a(2*-2)-(-3*1) + (-b)[(-1*-2)-(2*1)]+0[(-1*-3)-(2*2)]

=a(-1)-b(0)

=-a

But given $$det(P)$$ = -2

Hence a = 2

Minor of $$M_{22}$$ = $$det\begin{bmatrix}a & 0 \\2 & -2 \end{bmatrix}$$

det of $$\begin{bmatrix}2 & 0 \\2 & -2 \end{bmatrix}$$

= -4

Hence A is the correct answer.

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