Teaching MPPSC Assistant Professor Mock Test Series 2025 Mathematics Matrices Operations on Matrices
Let T : R3 → R3 be the linear transformation whose matrix with respect to the standard basis of R3 is \( \begin{bmatrix} {0} & {a} & b \\[0.3em] {-a} & 0 & c \ \\[0.3em] {-b} & {-c} & 0 \\[0.3em] \end{bmatrix} \), where a, b, c are real numbers not all zero. Then T
1
is one - one
2
is onto
3
does not map any line through the origin onto itself
4
has rank 1