Basics of Linear Algebra MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Basics of Linear Algebra”.

a) x=1, y=3, z=4, w=0
b) x=2, y=3, z=8, w=1
c) x=1, y=2, z=3, w=1
d) x=1, y=2, z=4, w=1


a) \begin{bmatrix} 1 & 4 \\ -2 & 9 \\ \end{bmatrix}
b) \begin{bmatrix} 1 & 4 \\ -2 & 9 \\ -3 & 8 \\ \end{bmatrix}
c) \begin{bmatrix} 1 & -2 & -3\\ 4 & 9 & 8\\ \end{bmatrix}
d) \begin{bmatrix} -1 & 2 & 3\\ -4 & -9 & 8\\ \end{bmatrix}

a) \frac{1}{13}*\begin{bmatrix} 90 & 65 & 80\\ 65 & 61 & 54\\ 80 & 58 & 69\\ \end{bmatrix}
b) \frac{1}{14}*\begin{bmatrix} 93 & 68 & 80\\ 68 & 61 & 58\\ 80 & 58 & 69\\ \end{bmatrix}
c) \frac{1}{13}*\begin{bmatrix} 94 & 67 & 80\\ 67 & 60 & 56\\ 80 & 58 & 69\\ \end{bmatrix}
d) \frac{1}{13}*\begin{bmatrix} 93 & 68 & 80\\ 68 & 61 & 58\\ 80 & 58 & 69\\ \end{bmatrix}

4. Find the adjacent A as A=\begin{bmatrix} 1 & 7 & -3\\ 5 & 4 & -2\\ 6 & 8 & -6\\ \end{bmatrix}.
a) \begin{bmatrix} 1 & 1 & 1\\ 1 & 2 & 3\\ 2 & 3 & 4\\ \end{bmatrix}
b) \begin{bmatrix} 31 & 39 & 80\\ 39 & 45 & 74\\ 80 & 74 & 136\\ \end{bmatrix}
c) \begin{bmatrix} 1 & 0 & 0\\ 0 & 1 & 0\\ 0 & 0 & 1\\ \end{bmatrix}
d) \begin{bmatrix} 35 & 34 & 32\\ 56 & 67 & 48\\ 98 & 74 & 52\\ \end{bmatrix}

5. Given the equations are 4x+2y+z=8, x+ y+ z=3, 3x+y+3z=9. Find the values of x, y and z.
a) 5/3, 0, 2/3
b) 1, 2, 3
c) 4/3, 1/3, 5/3
d) 2, 3, 4

6. The rank of the matrix (m × n) where m<n cannot be more than?
a) m
b) n
c) m*n
d) m-n

7. Find the rank of the matrix A=\begin{bmatrix} 1 & 3 & 5\\ 4 & 6 & 7\\ 1 & 2 & 2\\ \end{bmatrix}.
a) 3
b) 2
c) 1
d) 0

8. For the following set of simultaneous equations 1.5x-0.5y=2, 4x+2y+3z=9, 7x+y+5=10.
a) The solution is unique
b) Infinitely many solutions exist
c) The equations are incompatible
d) Finite number of multiple solutions exist

9. Given A=\begin{bmatrix} 2 & -0.1 \\ 0 & 3 \\ \end{bmatrix} A^{-1} = \begin{bmatrix} 1/2 & a \\ 0 & b \\ \end{bmatrix} then find a + b.
a) \frac{6}{20}
b) \frac{7}{20}
c) \frac{8}{20}
d) \frac{5}{20}

10. If a square matrix B is skew symmetric then.
a) BT = -B
b) BT = B
c) B-1 = B
d) B-1 = BT

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