Find the determinant of the 3x3 matrix ( A = begin{bmatrix} 1 & 2 & 3 4 & 5 & 6 7 & 8 & 9 end{bmatrix} )

Question

Find the determinant of the 3x3 matrix ( A = begin{bmatrix} 1 & 2 & 3  4 & 5 & 6  7 & 8 & 9 end{bmatrix} )

Accepted Answer

Step:1 ：The determinant of a 3x3 matrix ( A = begin{bmatrix} a & b & c  d & e & f  g & h & i end{bmatrix} ) is given by ( det(A) = aei + bfg + cdh - ceg - bdi - afh ).Step:2 ：Substituting the given values, we get ( det(A) = 1*5*9 + 2*6*7 + 3*4*8 - 3*5*7 - 2*4*9 - 1*6*8 ).Step:3 ：Solving this, we get ( det(A) = 45 + 84 + 96 - 105 - 72 - 48 ).Step:4 ：Simplifying, we get ( det(A) = 0 ).

Answer

Step: 1 ：The determinant of a 3x3 matrix ( A = begin{bmatrix} a & b & c  d & e & f  g & h & i end{bmatrix} ) is given by ( det(A) = aei + bfg + cdh - ceg - bdi - afh ).Step: 2 ：Substituting the given values, we get ( det(A) = 1*5*9 + 2*6*7 + 3*4*8 - 3*5*7 - 2*4*9 - 1*6*8 ).Step: 3 ：Solving this, we get ( det(A) = 45 + 84 + 96 - 105 - 72 - 48 ).Step: 4 ：Simplifying, we get ( det(A) = 0 ).

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

Answer

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