Find the determinant of the 3x3 matrix: [A = begin{bmatrix} 2 & 5 & -3 1 & -2 & 2 0 & 5 & -1 end{bmatrix}]

Question

Find the determinant of the 3x3 matrix: [A = begin{bmatrix} 2 & 5 & -3  1 & -2 & 2  0 & 5 & -1 end{bmatrix}]

Accepted Answer

Step:1 ：Step 1: Use the formula for finding the determinant of a 3x3 matrix, which is: [det(A) = a(ei−fh)−b(di−fg)+c(dh−eg)] where a, b, c, d, e, f, g, h, and i are the elements of the matrix.Step:2 ：Step 2: Substitute the matrix elements into the formula: [det(A) = 2((-2)*(-1)−(2*5))−5((1)*(-1)−(2*0))+(-3)((1)*(5)−(-2*0))]Step:3 ：Step 3: Simplify the above expression: [det(A) = 2*(2−10)−5*(-1)+(-3)*(5) = 2*(-8) + 5 +(-15) = -16 + 5 -15]

Answer

Step: 1 ：Step 1: Use the formula for finding the determinant of a 3x3 matrix, which is: [det(A) = a(ei−fh)−b(di−fg)+c(dh−eg)] where a, b, c, d, e, f, g, h, and i are the elements of the matrix.Step: 2 ：Step 2: Substitute the matrix elements into the formula: [det(A) = 2((-2)*(-1)−(2*5))−5((1)*(-1)−(2*0))+(-3)((1)*(5)−(-2*0))]Step: 3 ：Step 3: Simplify the above expression: [det(A) = 2*(2−10)−5*(-1)+(-3)*(5) = 2*(-8) + 5 +(-15) = -16 + 5 -15]

Find the determinant of the 3x3 matrix: \[A = \begin{bmatrix} 2 & 5 & -3 \ 1 & -2 & 2 \ 0 & 5 & -1 \end{bmatrix}\]

Answer

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