Linear Algebra MCQs Question and Answer in Engineering Maths

The eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 4&{ - 2} \\ { - 2}&1 \end{array}} \right]\]

For the set of equations
x₁ + 2x₂ + x₃ + 4x₄ = 2
3x₁ + 6x₂ + 3x₃ + 12x₄ = 6
the following statement is true:

Let A be an m × n matrix and Ban n × m matrix. It is given that determinant ($$I$$_m + AB) = determinant ($$I$$_n + BA), where $$I$$_k is the k × k identity matrix. Using the above property, the determinant of the matrix given below is
\[\left[ {\begin{array}{*{20}{c}} 2&1&1&1 \\ 1&2&1&1 \\ 1&1&2&1 \\ 1&1&1&2 \end{array}} \right]\]