If the matrix P = \begin{pmatrix} x & 3 \\ 8 & 6 \end{pmatrix} is a singular matrix, what … — JAMB UTME

If the matrix $P = \begin{pmatrix} x & 3 \\ 8 & 6 \end{pmatrix}$ is a singular matrix, what is the value of $x$ ?

The value of

x

4

For a

2 \times 2

matrix to be singular, its determinant must be zero. For matrix

P

, the determinant is

(x \cdot 6) - (3 \cdot 8) = 6x - 24

. Setting

6x - 24 = 0

gives

6x = 24

, which simplifies to

x = 4

State the condition for a matrix to be singular.

A matrix is singular if its determinant is equal to zero:

\det(P) = 0

By definition, a singular matrix has a determinant equal to zero.

Calculate the determinant of matrix

P

\det(P) = (x \times 6) - (3 \times 8) = 6x - 24.

The determinant of a

2 \times 2

matrix

\begin{pmatrix} a & b \\ c & d \end{pmatrix}

is calculated using the formula

ad - bc

Solve the linear equation

6x - 24 = 0

for

x

6x = 24 \implies x = 4.

Adding

24

to both sides and dividing by

6

isolates

x

Singular matrix condition and

2 \times 2

determinant calculation

Question