MTH501 - Linear Algebra

All MCQs Tests - VU MTH501 - Linear Algebra

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Subject	MTH501 - Linear Algebra			Chapter / Term	All MCQs
Quiz No	1	Total Time	10 Minute(s)	No. of Questions	10 Question(s)

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Chapter / Term

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Question(s)

Q1

Question 1: Which of the following will be the Linear Combination corresponding to $\begin{pmatrix} -2 & 3 \ 5 & 1 \ end{pmatrix}\begin{pmatrix} x \ y \ end{pmatrix} $?

$$ egin{pmatrix} -2 \ 3 \ end{pmatrix} x + egin{pmatrix} 5 \ 1 \ end{pmatrix} y $$

$$ egin{pmatrix} 3 \ 1 \ end{pmatrix} x + egin{pmatrix} -2 \ 5 \ end{pmatrix} y $$

$$ egin{pmatrix} 5 \ 1 \ end{pmatrix} x + egin{pmatrix} -2 \ 3 \ end{pmatrix} y $$

$$ egin{pmatrix} -2 \ 5 \ end{pmatrix} x + egin{pmatrix} 3 \ 1 \ end{pmatrix} y $$

Q2

Question 2: Gauss-Seidel method is also termed as a method of

Elimination Method

False Position Method

Successive Displacement

Iteration Method

Q3

Question 3: If $v_1^r, v_2^r $ and $v_3^r $ are in $R^m $ then which of the following is equivalent to $\begin{bmatrix} v_1 & v_2 & v_3 \ end{bmatrix}\begin{bmatrix} 2 \ -7 \ 5 \ end{bmatrix} $

$$2v_1^r - 7v_2^r + 5v_3^r $$

$$5v_1^r - 7v_2^r + 2v_3^r $$

$$5v_1^r + 2v_2^r - 7v_3^r $$

$$2v_1^r + 5v_2^r - 7v_3^r $$

Q4

Question 4: If $ v_1^r = (2, 1), v_2^r = (3, 4) $ and $ v_3^r = (7, 8) $ then which of the following is true?

$$ {v_1^r, v_2^r, v_3^r} $$ is linearly dependent.

$$ {v_1^r, v_2^r, v_3^r} $$ is linearly independent.

The vector equation has trivial solution.

$$ v_1^r = {2 over 3} v_2^r $$

Q5

Question 5: If $ A =\begin{bmatrix} 2 & 3 & 5 \ 0 & 3 & 6 \ 0 & 0 & 4 \ end{bmatrix} $, then which of the following is the value of det(A)?

Q6

Question 6: If T be a transformation, then which of the following is true for its linearity?

$$ T(cu^r , gdv^r) = cT(u^r) gd T(v^r) ; ;;;; $$ whre 'c' and 'd' are scalars

$$ T(cu^r + dv^r) = cT(u^r) + dT(v^r); ;;;; $$ whre 'c' and 'd' are scalars

$$ T(cu^r × dv^r) = cT(u^r) × dT(v^r); ;;;; $$ whre 'c' and 'd' are scalars

$$ T(cu^r + dv^r) = dT(u^r) + cT(v^r); ;;;; $$ whre 'c' and 'd' are scalars

Q7

Question 7: Which of the following is the coefficient matrix for the system $\begin{matrix} x_1 - 2x_2 + x_3 = 0 \ 2x_2 - 7x_3 = 8 \ -4x_1 + 3x_2 + 9x_3 = -6 end{matrix} $

$$ egin{bmatrix} 1 & -2 & 1 \ 0 & 2 & -7 \ -4 & 3 & 9 \ end{bmatrix} $$

$$ egin{bmatrix} 1 & -2 & 0 \ 0 & 2 & 8 \ -4 & 3 & -6 \ end{bmatrix} $$

$$ egin{bmatrix} 1 & 1 & 0 \ 0 & -7 & 8 \ -4 & 9 & -6 \ end{bmatrix} $$

$$ egin{bmatrix} 1 & 0 & -4 \ -2 & 2 & 3 \ 1 & -7 & 9 \ end{bmatrix} $$