Question

The determinant of the matrix \[ \left[ \begin{array}{ccc} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{array} \right] \] is ........... 
 

Hint:

When calculating the determinant of a 3x3 matrix, remember to use cofactor expansion and simplify each step carefully.

Answer 1

Correct Answer: -7.9 - -8.1

To calculate the determinant of the given matrix \( \begin{bmatrix} 1 & 3 & 0 \\ 2 & 6 & 4 \\ -1 & -1 & 2 \end{bmatrix} \), we apply the formula for a 3x3 matrix determinant:

\(\text{det}(A) = a(ei − fh) − b(di − fg) + c(dh − eg)\)

Assigning values from the matrix:

• \(a = 1\), \(b = 3\), \(c = 0\)
• \(d = 2\), \(e = 6\), \(f = 4\)
• \(g = -1\), \(h = -1\), \(i = 2\)

Substitute these values into the formula:

• \(ei - fh = (6 \times 2) - (4 \times -1) = 12 + 4 = 16\)
• \(di - fg = (2 \times 2) - (4 \times -1) = 4 + 4 = 8\)
• \(dh - eg = (2 \times -1) - (6 \times -1) = -2 + 6 = 4\)

Thus,

\(\text{det}(A) = 1 \times 16 - 3 \times 8 + 0 \times 4\)

Calculate:

\(\text{det}(A) = 16 - 24 = -8\)