Find the determinant of the matrix n[ A = begin{bmatrix} 5 & 2 & 1 & 3 4 & 3 & 2 & 1 1 & 2 & 3 & 4 3 & 1 & 2 & 5 end{bmatrix} ]

Question

Find the determinant of the matrix n[ A = begin{bmatrix} 5 & 2 & 1 & 3  4 & 3 & 2 & 1  1 & 2 & 3 & 4  3 & 1 & 2 & 5 end{bmatrix} ]

Accepted Answer

Step:1 ：First, we perform row operations to simplify the matrix: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 1 & 2 & 1  0 & -1 & 1 & 2 end{bmatrix} ]Step:2 ：Next, we subtract row 2 from row 3 and add row 2 to row 4 to get: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 0 & 1 & 4  0 & 0 & 2 & -1 end{bmatrix} ]Step:3 ：Finally, we subtract 2*row 3 from row 4 to get: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 0 & 1 & 4  0 & 0 & 0 & -9 end{bmatrix} ]Step:4 ：The determinant of a triangular matrix is the product of its diagonal elements. So, the determinant of A is: n[ 5*1*1*-9 = -45 ]

Answer

Step: 1 ：First, we perform row operations to simplify the matrix: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 1 & 2 & 1  0 & -1 & 1 & 2 end{bmatrix} ]Step: 2 ：Next, we subtract row 2 from row 3 and add row 2 to row 4 to get: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 0 & 1 & 4  0 & 0 & 2 & -1 end{bmatrix} ]Step: 3 ：Finally, we subtract 2*row 3 from row 4 to get: n[ begin{bmatrix} 5 & 2 & 1 & 3  0 & 1 & 1 & -3  0 & 0 & 1 & 4  0 & 0 & 0 & -9 end{bmatrix} ]Step: 4 ：The determinant of a triangular matrix is the product of its diagonal elements. So, the determinant of A is: n[ 5*1*1*-9 = -45 ]

Find the determinant of the matrix \n $A = [\begin{matrix} 5 & 2 & 1 & 3 \\ 4 & 3 & 2 & 1 \\ 1 & 2 & 3 & 4 \\ 3 & 1 & 2 & 5 \end{matrix}]$

Answer

Popular Problems

Find the determinant of the matrix \nA=[5213432112343125]

Answer

Popular Problems

Find the determinant of the matrix \n $A = [\begin{matrix} 5 & 2 & 1 & 3 \\ 4 & 3 & 2 & 1 \\ 1 & 2 & 3 & 4 \\ 3 & 1 & 2 & 5 \end{matrix}]$