Find the determinant of the following 3x3 matrix: [ A = begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 end{bmatrix} ]

Question

Find the determinant of the following 3x3 matrix: [ A = begin{bmatrix} 1 & 2 & 3  4 & 5 & 6  7 & 8 & 9 end{bmatrix} ]

Accepted Answer

Step:1 ：First, we can use the formula for the determinant of a 3x3 matrix: ( det(A) = aei + bfg + cdh - ceg - bdi - afh ) where a, b, c, d, e, f, g, h, i are the elements of the matrix.Step:2 ：Substitute the elements of the matrix into the formula: ( det(A) = (1*5*9) + (2*6*7) + (3*4*8) - (3*5*7) - (2*4*9) - (1*6*8) )Step:3 ：Calculate the above expression: ( det(A) = 45 + 84 + 96 - 105 - 72 - 48 )Step:4 ：Simplify the above expression to get the final answer: ( det(A) = 0 )

Answer

Step: 1 ：First, we can use the formula for the determinant of a 3x3 matrix: ( det(A) = aei + bfg + cdh - ceg - bdi - afh ) where a, b, c, d, e, f, g, h, i are the elements of the matrix.Step: 2 ：Substitute the elements of the matrix into the formula: ( det(A) = (1*5*9) + (2*6*7) + (3*4*8) - (3*5*7) - (2*4*9) - (1*6*8) )Step: 3 ：Calculate the above expression: ( det(A) = 45 + 84 + 96 - 105 - 72 - 48 )Step: 4 ：Simplify the above expression to get the final answer: ( det(A) = 0 )

Find the determinant of the following 3x3 matrix: \[ A = \begin{bmatrix} 1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9 \end{bmatrix} \]

Answer

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