The determinant of E is 0 because the rows are linearly dependent.

The determinant of G is (2*3) - (4*1) = 6 - 4 = 2.

The determinant can be calculated using the formula for 3x3 matrices. Here, the first column is the same, leading to a determinant of 0.

The determinant of J is (2*5) - (3*4) = 10 - 12 = -2.

The determinant of J is (5*8) - (6*7) = 40 - 42 = -2.

The determinant is calculated as (0*0) - (1*1) = 0 - 1 = -1.

The determinant of a 2x2 matrix \( A = \begin{pmatrix} a & b \\ c & d \end{pmatrix} \) is given by \( ad - bc \). Here, \( 1*4 - 2*3 = 4 - 6 = -2 \).

The determinant of a diagonal matrix is the product of its diagonal elements: \( 5*7 = 35 \).

The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).

The determinant is 0 because the first column is a linear combination of the other columns.

The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).

The determinant of an upper triangular matrix is the product of its diagonal elements: \( 1*1*1 = 1 \).

Using the determinant formula for 3x3 matrices, we find \( 1(1*0 - 4*6) - 2(0*0 - 4*5) + 3(0*6 - 1*5) = 1(0 - 24) - 2(0 - 20) + 3(0 - 5) = -24 + 40 - 15 = 1 \).

The determinant is 0 because the rows are linearly dependent.

The determinant is calculated as \( 2*7 - 5*3 = 14 - 15 = -1 \).

The determinant is \( 2*7 - 3*5 = 14 - 15 = -1 \).

The determinant of the identity matrix is always 1.

The determinant of this matrix is 0 because the rows are linearly dependent.

The determinant is 0 because the rows are linearly dependent.

The determinant is \( 4*3 - 2*1 = 12 - 2 = 10 \).

Det(J) = (5*8) - (6*7) = 40 - 42 = -2.

The determinant of the identity matrix is 1.

The determinant is calculated as (1*1) - (1*1) = 1 - 1 = 0.

The determinant is calculated as \( 1(1*1 - 0*3) - 2(0*1 - 0*2) + 1(0*3 - 1*2) = 1 - 0 - 2 = -1 \).

The determinant is 0 because the rows are linearly dependent.

The determinant is calculated as \( 1*4 - 2*3 = 4 - 6 = -2 \).

The determinant is calculated as \( 1*5 - 2*3 = 5 - 6 = -1 \).

The determinant is calculated as (3*4) - (2*1) = 12 - 2 = 10.

The determinant is calculated as \( 5*8 - 6*7 = 40 - 42 = -2 \).

Calculating gives a determinant of -3.