Let matrix A= x y -z 1 2 3 1 1 2 , where x, y, z∈N. If adjadjadjadjA=4^8·5^16, then the number of such matrices A is equal to (where, M represents…

Question

Let matrix A= x y -z 1 2 3 1 1 2 , where x, y, z∈N. If adjadjadjadjA=4^8·5^16, then the number of such matrices A is equal to (where, M represents determinant of a matrix M)

MARKS Content Team · Accepted Answer

Correct answer: 36. det.adjadjadjadjA=A^(3-14) =A^16=4^8.5^16 ⇒A=±10 A= x y -z 1 2 3 1 1 2 =x+y+z=±10 ∵x,y,z∈N⇒x+y+z=-10 (not possible) Hence, x+y+z=10 The number of such matrices =^9C_2 =36

Let matrix $A = [\begin{matrix} x & y & - z \\ 1 & 2 & 3 \\ 1 & 1 & 2 \end{matrix}]$ , where $x, y, z \in N$ . If $|adj |adj |adj |adjA|||| = 4^{8} \cdot 5^{16}$ , then the number of such matrices $A$ is equal to (where, $|M|$ represents determinant of a matrix $M$ )

Solution

More Determinants Questions

Let matrix A=xy-z12 311 2, where x, y, z∈N. If adjadjadjadjA=48·516, then the number of such matrices A is equal to (where, M represents determinant of a matrix M)

Solution

More Determinants Questions

Let matrix $A = [\begin{matrix} x & y & - z \\ 1 & 2 & 3 \\ 1 & 1 & 2 \end{matrix}]$ , where $x, y, z \in N$ . If $|adj |adj |adj |adjA|||| = 4^{8} \cdot 5^{16}$ , then the number of such matrices $A$ is equal to (where, $|M|$ represents determinant of a matrix $M$ )