PYQs Based Test - 01 : Matrix Algebra and System of Linear Equati..

If the following system has non-trivial solution,

px + qy + rz = 0

qx + ry + pz = 0

rx + py + qz = 0,

then which one of the following options is TRUE?

The matrix = ≤ft[ {*20c &0&3&7\\ 2&5&1&3\\ 0&0&2&4\\ 0&0&0&} ] has $\det (\mathrm{A})=100$ and $\mathrm{trace}(\mathrm{A})=14$.

The value of $|a-b|$ is ________.

Given that the determinant of the matrix ≤ft[ {*20c 1&3&0\\ 2&6&4\\ - 1&0&2 } ] is -12, the determinant of the matrix ≤ft[ {*20c 2&6&0\\ 4&12&8\\ - 2&0&4 } ] is

The maximum value of the determinant among all 2 × 2 real symmetric matrices with trace 24 is _______.

The rank of the matrix

≤ft[ {*20c 1& - 1&0&0&0\\ 0&0&1& - 1&0\\ 0&1& - 1&0&0\\ - 1&0&0&0&1\\ 0&0&0&1& - 1 } ]