Find the determinant of the following matrix: [ A = begin{bmatrix} 4 & 3 & 2 3 & 2 & 1 2 & 1 & 4 end{bmatrix} ]

Question

Find the determinant of the following matrix: [ A = begin{bmatrix} 4 & 3 & 2  3 & 2 & 1  2 & 1 & 4 end{bmatrix} ]

Accepted Answer

Step:1 ：The determinant of a 3x3 matrix can be calculated using the formula: [ det(A) = a(ei−fh)−b(di−fg)+c(dh−eg) ] where [ A = begin{bmatrix} a & b & c  d & e & f  g & h & i end{bmatrix} ]Step:2 ：Substituting the values from matrix A into the formula, we get: [ det(A) = 4(2*4−1*1)−3(3*4−2*1)+2(3*1−2*2) ]Step:3 ：Calculating the above expression, we get: [ det(A) = 4(8−1)−3(12−2)+2(3−4) ]Step:4 ：Further simplifying, we get: [ det(A) = 4*7−3*10+2*(-1) ]Step:5 ：Finally, we have: [ det(A) = 28−30−2 ]

Answer

Step: 1 ：The determinant of a 3x3 matrix can be calculated using the formula: [ det(A) = a(ei−fh)−b(di−fg)+c(dh−eg) ] where [ A = begin{bmatrix} a & b & c  d & e & f  g & h & i end{bmatrix} ]Step: 2 ：Substituting the values from matrix A into the formula, we get: [ det(A) = 4(2*4−1*1)−3(3*4−2*1)+2(3*1−2*2) ]Step: 3 ：Calculating the above expression, we get: [ det(A) = 4(8−1)−3(12−2)+2(3−4) ]Step: 4 ：Further simplifying, we get: [ det(A) = 4*7−3*10+2*(-1) ]Step: 5 ：Finally, we have: [ det(A) = 28−30−2 ]

Find the determinant of the following matrix: \[ A = \begin{bmatrix} 4 & 3 & 2 \\ 3 & 2 & 1 \\ 2 & 1 & 4 \end{bmatrix} \]

Answer

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