What is the determinant of the 2 \times 2 matrix P = \begin{pmatrix} 5 & 2 \\ 3 & 4 \end{p… — JAMB UTME

What is the determinant of the $2 \times 2$ matrix $P = \begin{pmatrix} 5 & 2 \\ 3 & 4 \end{pmatrix}$ ?

Answer: 14

The determinant of matrix

P

14

For any

2 \times 2

matrix

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

, the determinant is given by

ad - bc

. Substituting

a=5

b=2

c=3

, and

d=4

yields

(5 \times 4) - (2 \times 3) = 20 - 6 = 14

Apply the determinant formula for a

2 \times 2

matrix

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

, which is

\det(P) = ad - bc

\det(P) = (5)(4) - (2)(3)

The determinant of a

2 \times 2

matrix is defined as the product of the main diagonal elements minus the product of the off-diagonal elements.

Evaluate the arithmetic expression.

20 - 6 = 14

Perform multiplication followed by subtraction to get the final determinant value.

Determinant of a 2x2 Matrix

Estimated Time:45s

Question