Linear Algebra MCQs Question and Answer in Engineering Maths

The matrix P is the inverse of a matrix Q. If $$I$$ denotes the identity matrix, which one of the following options is correct?

A square matrix B is skew-symmetric if

Given that, \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} { - 5}&{ - 3} \\ 2&0 \end{array}} \right]\]   and \[I = \left[ {\begin{array}{*{20}{c}} 1&0 \\ 0&1 \end{array}} \right],\]   the value A³ is

Consider the matrices X_{(4 × 3)}, Y_{(4 × 3)} and P_{(2 × 3)}. The order of [P(X^TY)^-1 P^T]^T will be

The rank of the matrix \[\left[ {\begin{array}{*{20}{c}} { - 4}&1&{ - 1} \\ { - 1}&{ - 1}&{ - 1} \\ 7&{ - 3}&1 \end{array}} \right]\]   is

Consider the following linear system.
x + 2y - 3z = a
2x + 3y + 3z = b
5x + 9y - 6z = c
This system is consistent if a, b and c satisfy the equation

Consider a 3 × 3 real symmetric matrix S such that two of its eigen values are a ≠ 0, b ≠ 0 with respective eigen vectors \[\left[ {\begin{array}{*{20}{c}} {{{\text{x}}_1}} \\ {{{\text{x}}_2}} \\ {{{\text{x}}_3}} \end{array}} \right],\left[ {\begin{array}{*{20}{c}} {{{\text{y}}_1}} \\ {{{\text{y}}_2}} \\ {{{\text{y}}_3}} \end{array}} \right].\]   If a ≠ b then x₁y₁ + x₂y₂ + x₃y₃ equals

For which value of x will the matrix given below become singular?
\[\left[ {\begin{array}{*{20}{c}} 8&{\text{x}}&0 \\ 4&0&2 \\ {12}&6&0 \end{array}} \right]\]

The number of solutions of the simultaneous algebraic equation y = 3x + 3 and y = 3x + 5 is:

Given Matrix \[\left[ {\text{A}} \right] = \left[ {\begin{array}{*{20}{c}} 4&2&1&3 \\ 6&3&4&7 \\ 2&1&0&1 \end{array}} \right],\]     the rank of the matrix is