If the matrix P = \begin{pmatrix} k & 2 & 0 \\ 1 & 4 & 1 \\ 3 & 0 & 2 \end{pmatrix} has a … — JAMB UTME

If the matrix $P = \begin{pmatrix} k & 2 & 0 \\ 1 & 4 & 1 \\ 3 & 0 & 2 \end{pmatrix}$ has a determinant equal to $18$ , find the value of $k$ .

Answer: 2

The value of

k

2

Expanding matrix

P

along the first row gives

\det(P) = k(8 - 0) - 2(2 - 3) + 0(0 - 12) = 8k + 2

. Setting

8k + 2 = 18

yields

8k = 16

, which simplifies to

k = 2

Expand the matrix determinant along the first row.

\det(P) = k(8 - 0) - 2(2 - 3) + 0 = 8k + 2

Applying the cofactor expansion formula for a

3 \times 3

matrix across row 1.

Set the resulting determinant expression equal to the given value of 18.

8k + 2 = 18

The question specifies that the determinant of

P

is equal to

18

Solve the linear equation for

k

k = 2

Subtracting 2 from both sides yields

8k = 16

, and dividing by 8 gives

k = 2

Determinant of a

3 \times 3

Matrix

Question