Linear Algebra MCQs Question and Answer in Engineering Maths

The sum of Eigen values of matrix, [M] is where \[\left[ {\text{M}} \right] = \left[ {\begin{array}{*{20}{c}} {215}&{650}&{795} \\ {655}&{150}&{835} \\ {485}&{355}&{550} \end{array}} \right]\]

The set of equations
x + y + z = 1
ax - ay + 3z = 5
5x - 3y + az = 6
has infinite solution if a = ?

Consider the system of equations A_{(n × n)} X_{(n × 1)} = λ_{(n × 1)} where, λ is a scalar. Let (λ_i, x_i) be an eigen-pair of an eigen value and its corresponding eigen vector for real matrix A. Let $$I$$ be a (n × n) unit matrix. Which one of the following statement is NOT correct?

The value of x for which all the eigen-values of the matrix given below are real is \[\left[ {\begin{array}{*{20}{c}} {10}&{5 + {\text{j}}}&4 \\ {\text{x}}&{20}&2 \\ 4&2&{ - 10} \end{array}} \right]\]

The system of linear equations \[\left[ {\begin{array}{*{20}{c}} 2&1&3 \\ 3&0&1 \\ 1&2&5 \end{array}} \right]\left[ {\begin{array}{*{20}{c}} {\text{a}} \\ {\text{b}} \\ {\text{c}} \end{array}} \right] = \left[ {\begin{array}{*{20}{c}} 5 \\ { - 4} \\ {14} \end{array}} \right]\]     has

The matrix \[{\text{P}} = \left[ {\begin{array}{*{20}{c}} 0&0&1 \\ 1&0&0 \\ 0&1&0 \end{array}} \right]\]   rotates a vector about the axis \[\left[ {\begin{array}{*{20}{c}} 1 \\ 1 \\ 1 \end{array}} \right]\] by angle of

If a square matrix of order 100 has exactly 15 distinct eigen values, the degree of the minimal polynomial is

A matrix has eigen values -1 and -2. The corresponding eigen vectors are \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \end{array}} \right]\] and \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 2} \end{array}} \right]\] respectively. The matrix is

Let A, B, C, D be n × n matrices, each with nonzero determinant, If ABCD = $$I$$, then B^-1 is

The eigen vectors of the matrix \[\left[ {\begin{array}{*{20}{c}} 1&2 \\ 0&2 \end{array}} \right]\]  are written in the form \[\left[ {\begin{array}{*{20}{c}} 1 \\ {\text{a}} \end{array}} \right]\] and \[\left[ {\begin{array}{*{20}{c}} 1 \\ {\text{b}} \end{array}} \right].\]  What is a + b = ?