Linear Algebra MCQs Question and Answer in Engineering Maths

1.
If $${\left[ {1,\,0,\, - 1} \right]^{\text{T}}}$$ is an eigen vector of the following matrix \[\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0 \\ { - 1}&2&{ - 1} \\ 0&{ - 1}&1 \end{array}} \right]\] then corresponding eigen value is

A. 1

B. 2

C. 3

D. 5

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2.
The eigen values of the following matrix are \[\left[ {\begin{array}{*{20}{c}} { - 1}&3&5 \\ { - 3}&{ - 1}&6 \\ 0&0&3 \end{array}} \right]\]

A. 3, 3 + 5j, 6 - j

B. -6 + 5j, 3 + j, 3 - j

C. 3 + j, 3 - j, 5 + j

D. 3, -1 + 3j, -1 - 3j

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3.
Let A be the 2 × 2 matrix with elements a₁₁ = a₁₂ = a₂₁ = +1 and a₂₂ = -1. Then the eigen values of the matrix A¹⁹ are

A. 1024 and -1024

B. 1024√2 and -1024√2

C. 4√2 and -4√2

D. 512√2 and -512√2

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4.
How many of the following matrices have an eigen value 1?
\[\left[ {\begin{array}{{20}{c}} 1&0 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{{20}{c}} 0&1 \\ 0&0 \end{array}} \right],\left[ {\begin{array}{{20}{c}} 1&{ - 1} \\ 1&1 \end{array}} \right]{\text{ and }}\left[ {\begin{array}{{20}{c}} { - 1}&0 \\ 1&{ - 1} \end{array}} \right]\]

A. one

B. two

C. three

D. four

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5.
A real square matrix A is called skew-symmetric if

A. A^T = A

B. A^T = A^-1

C. A^T = -A

D. A^T = A + A^-1

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6.
If \[{\text{R}} = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 1} \\ 2&1&{ - 1} \\ 2&3&2 \end{array}} \right],\] then top row of R^-1 is

A. [5 6 4]

B. [5 -3 1]

C. [2 0 -1]

D. \[\left[ {\begin{array}{*{20}{c}} 2&{ - 1}&{\frac{1}{2}} \end{array}} \right]\]

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7.
Let, \[{\text{A}} = \left[ {\begin{array}{{20}{c}} 2&{ - 0.1} \\ 0&3 \end{array}} \right]\] and \[{{\text{A}}^{ - 1}} = \left[ {\begin{array}{{20}{c}} {\frac{1}{2}}&{\text{a}} \\ 0&{\text{b}} \end{array}} \right].\]
Then (a + b) = ?

A. \[\frac{7}{{20}}\]

B. \[\frac{3}{{20}}\]

C. \[\frac{{19}}{{60}}\]

D. \[\frac{{11}}{{20}}\]

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8.
We have a set of 3 linear equations in 3 unknowns. 'X \[ \equiv \] Y' means X and Y are equivalent statements and 'X \[\not \equiv \] Y' means X and Y are not equivalent statements.
P : There is a unique solution.
Q : The equations are linearly independent.
R : All eigen values of the coefficient matrix are nonzero.
S : The determinant of the coefficient matrix is nonzero.
Which one of the following is TRUE?

A. \[{\text{P}} \equiv {\text{Q}} \equiv {\text{R}} \equiv {\text{S}}\]

B. \[{\text{P}} \equiv {\text{R}}\not \equiv {\text{Q}} \equiv {\text{S}}\]

C. \[{\text{P}} \equiv {\text{Q}}\not \equiv {\text{R}} \equiv {\text{S}}\]

D. \[{\text{P}}\not \equiv {\text{Q}}\not \equiv {\text{R}}\not \equiv {\text{S}}\]

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9.
The elgen values of the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&{ - 1}&5 \\ 0&5&6 \\ 0&{ - 6}&5 \end{array}} \right]\] are

A. -1, 5, 6

B. 1, -5, ±j6

C. 1, 5, ±j6

D. 1, 5, 5

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10.
Consider the following simultaneous equations (with c₁ and c₂ being constants):
3x₁ + 2x₂ = c₁
4x₁ + x₂ = c₂
The characteristics equation for these simultaneous equations is

A. \[{\lambda ^2} - 4\lambda - 5 = 0\]

B. \[{\lambda ^2} - 4\lambda + 5 = 0\]

C. \[{\lambda ^2} + 4\lambda - 5 = 0\]

D. \[{\lambda ^2} + 4\lambda + 5 = 0\]

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Linear Algebra MCQs Question and Answer in Engineering Maths

1. If $${\left[ {1,\,0,\, - 1} \right]^{\text{T}}}$$ is an eigen vector of the following matrix \[\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0 \\ { - 1}&2&{ - 1} \\ 0&{ - 1}&1 \end{array}} \right]\] then corresponding eigen value is

Answer & Solution

2. The eigen values of the following matrix are \[\left[ {\begin{array}{*{20}{c}} { - 1}&3&5 \\ { - 3}&{ - 1}&6 \\ 0&0&3 \end{array}} \right]\]

Answer & Solution

3. Let A be the 2 × 2 matrix with elements a11 = a12 = a21 = +1 and a22 = -1. Then the eigen values of the matrix A19 are

Answer & Solution

Answer & Solution

5. A real square matrix A is called skew-symmetric if

Answer & Solution

6. If \[{\text{R}} = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 1} \\ 2&1&{ - 1} \\ 2&3&2 \end{array}} \right],\] then top row of R-1 is

Answer & Solution

7. Let, \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 2&{ - 0.1} \\ 0&3 \end{array}} \right]\] and \[{{\text{A}}^{ - 1}} = \left[ {\begin{array}{*{20}{c}} {\frac{1}{2}}&{\text{a}} \\ 0&{\text{b}} \end{array}} \right].\] Then (a + b) = ?

Answer & Solution

Answer & Solution

9. The elgen values of the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&{ - 1}&5 \\ 0&5&6 \\ 0&{ - 6}&5 \end{array}} \right]\] are

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10. Consider the following simultaneous equations (with c1 and c2 being constants): 3x1 + 2x2 = c1 4x1 + x2 = c2 The characteristics equation for these simultaneous equations is

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Read More Section(Linear Algebra)

1.
If $${\left[ {1,\,0,\, - 1} \right]^{\text{T}}}$$ is an eigen vector of the following matrix \[\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0 \\ { - 1}&2&{ - 1} \\ 0&{ - 1}&1 \end{array}} \right]\] then corresponding eigen value is

2.
The eigen values of the following matrix are \[\left[ {\begin{array}{*{20}{c}} { - 1}&3&5 \\ { - 3}&{ - 1}&6 \\ 0&0&3 \end{array}} \right]\]

3.
Let A be the 2 × 2 matrix with elements a₁₁ = a₁₂ = a₂₁ = +1 and a₂₂ = -1. Then the eigen values of the matrix A¹⁹ are

5.
A real square matrix A is called skew-symmetric if

6.
If \[{\text{R}} = \left[ {\begin{array}{*{20}{c}} 1&0&{ - 1} \\ 2&1&{ - 1} \\ 2&3&2 \end{array}} \right],\] then top row of R^-1 is

7.
Let, \[{\text{A}} = \left[ {\begin{array}{{20}{c}} 2&{ - 0.1} \\ 0&3 \end{array}} \right]\] and \[{{\text{A}}^{ - 1}} = \left[ {\begin{array}{{20}{c}} {\frac{1}{2}}&{\text{a}} \\ 0&{\text{b}} \end{array}} \right].\]
Then (a + b) = ?

9.
The elgen values of the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}} 1&{ - 1}&5 \\ 0&5&6 \\ 0&{ - 6}&5 \end{array}} \right]\] are

10.
Consider the following simultaneous equations (with c₁ and c₂ being constants):
3x₁ + 2x₂ = c₁
4x₁ + x₂ = c₂
The characteristics equation for these simultaneous equations is