What is the determinant of the matrix P = \begin{pmatrix} 5 & 3 \\ 2 & 7 \end{pmatrix}? — JAMB UTME

What is the determinant of the matrix $P = \begin{pmatrix} 5 & 3 \\ 2 & 7 \end{pmatrix}$ ?

Cevap: 29

For a

2 \times 2

matrix

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

, the determinant is given by

ad - bc

. Substituting the values

a = 5

b = 3

c = 2

, and

d = 7

yields

(5 \times 7) - (3 \times 2) = 35 - 6 = 29

Identify the values of

a, b, c,

and

d

from the given

2 \times 2

matrix

P = \begin{pmatrix} 5 & 3 \\ 2 & 7 \end{pmatrix}

a = 5, b = 3, c = 2, d = 7

To set up the values for the

2 \times 2

determinant formula.

Multiply the elements of the main diagonal and the secondary diagonal.

Main diagonal product:

5 \times 7 = 35

; Secondary diagonal product:

3 \times 2 = 6

The determinant of a

2 \times 2

matrix is the difference between the main diagonal product and the secondary diagonal product.

Subtract the product of the secondary diagonal from the product of the main diagonal.

Determinant =

35 - 6 = 29

Completes the formula

\det(P) = ad - bc

Determinant of a 2x2 Matrix

Soru