Given the 2 \times 2 matrix M = \begin{pmatrix} 7 & -2 \\ 4 & 3 \end{pmatrix}, what is the… — JAMB UTME

Given the $2 \times 2$ matrix $M = \begin{pmatrix} 7 & -2 \\ 4 & 3 \end{pmatrix}$ , what is the value of $\det(M)$ ?

Cevap: 29

The determinant of matrix

M

is 29.

The determinant of a

2 \times 2

matrix

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

is calculated as

ad - bc

. For the matrix

M = \begin{pmatrix} 7 & -2 \\ 4 & 3 \end{pmatrix}

, we compute

(7)(3) - (-2)(4) = 21 - (-8) = 29

Identify the entries

a, b, c, d

from the matrix

M = \begin{pmatrix} 7 & -2 \\ 4 & 3 \end{pmatrix}

a = 7

b = -2

c = 4

, and

d = 3

These entries correspond to the standard

2 \times 2

matrix representation

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

Compute the determinant using the formula

\det(M) = ad - bc

\det(M) = (7)(3) - (-2)(4) = 21 + 8 = 29

Multiplying the main diagonal entries and subtracting the product of the off-diagonal entries yields the determinant.

Determinant of a 2x2 Matrix

Soru