Linear Algebra MCQs Question and Answer in Engineering Maths

Which one of the following statements is true for all real symmetric matrices?

x + 2y + z = 4
2x + y + 2z = 5
x - y + z = 1
The system of algebraic given below has

Let P ≠ 0 be a 3 × 3 real matrix. There exist linearly independent vectors x and y such that PX = 0 and PY = 0. The dimension to the range space of P is

Consider the systems, each consisting of m linear equations in n variables.
I. If m < n, then all such systems have a solution.
II. If m > n, then none of these systems has a solution.
III. If m = n, then there exists a system which has a solution.
Which one of the following is CORRECT?

Consider the following system of linear equations
\[\left[ {\begin{array}{*{20}{c}} 2&1&{ - 4} \\ 4&3&{ - 12} \\ 1&2&{ - 8} \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \\ {\text{z}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} \alpha \\ 5 \\ 7 \end{array}} \right]\]
Notice that the second and the third columns of the coefficient matrix are linearly dependent. For how many values of \[\alpha \], does this system of equations have infinitely many solutions?

M is a 2 × 2 matrix with eigen values 4 and 9. The eigen values of M² are

The product of matrices (PQ)^-1P is

Let A be a 4 × 3 real matrix with rank 2. Which one of the following statement is TRUE?

The inverse of matrix \[\left[ {\begin{array}{*{20}{c}} 0&1&0 \\ 1&0&0 \\ 0&0&1 \end{array}} \right]\]  is

The trace and determinant of a 2 × 2 matrix are known to be -2 and -35 respectively. It eigen values are