Linear Algebra MCQs Question and Answer in Engineering Maths

The matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&{\frac{1}{2}} \\ 0&{ - 1}&0 \\ {\frac{1}{2}}&0&{\frac{3}{2}} \end{array}} \right]\]   has three distinct eigen values and one of its eigen vectors is \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ 1 \end{array}} \right].\]
Which one of the following can be another eigen vector of A?

The determinant \[\left| {\begin{array}{*{20}{c}} {1 + {\text{b}}}&{\text{b}}&1 \\ {\text{b}}&{1 + {\text{b}}}&1 \\ 2&{2{\text{b}}}&1 \end{array}} \right|\]    equals to

The solution of the system of equations x + y + z = 4, x - y + z = 0, 2x + y + z = 5 is

Which one of the following is an eigen vector of the matrix \[\left[ {\begin{array}{*{20}{c}} 5&0&0&0 \\ 0&5&5&0 \\ 0&0&2&1 \\ 0&0&3&1 \end{array}} \right]?\]

The system of equation, given below, has
x + 2y + 4z = 2
4x + 3y + z = 5
3x + 2y + 3z = 1

The characteristic equation of a (3 × 3) matrix P is defined as
a(λ) = |P - λ$$I$$| = λ³ + λ² + 2λ + 1 = 0
If $$I$$ denotes identity matrix, then the inverse of matrix P will be

For \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&{\tan \,{\text{x}}} \\ { - \tan {\text{ x}}}&1 \end{array}} \right],\]     the determinant of A^TA^-1 is

The value of the determinant \[\left| {\begin{array}{*{20}{c}} 1&3&2 \\ 4&1&1 \\ 2&1&3 \end{array}} \right|\]  is

The value of x₃ obtained by solving following system of linear equation is
x₁ + 2x₂ - 2x₃ = 4
2x₁ + x₂ + x₃ = -2
-x₁ + x₂ - x₃ = 2

For what values of α and β, the following simultaneous equations have an infinite number of solutions?
x + y + z = 5
x + 3y + 3z = 9
x + 2y + αz = β