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3 C 21545-A

If W is a subspace of a finite-dimensional vector space V, then :
(A) dim (W) = dim (V) always. (8) dim (W) 2 dim (V).
(ಲಿ) dim (W) < dim (४). (D) None of the above.
An x n matrix has:
(A) At most n distinct eigenvalues. (B) Atleast n distinct eigenvalues.
(C) Exactly n distinct eigenvalues. (D) Exactly n + 1 distinct eigenvalues.

Find the value of m such that the vector (m, 7, — 4) is alinear combination of vectors (— 2, 2, 1) and

(2, 1, -2):
(^) 2. (8) - 2.
(C) 0. (൬) -1.

Suppose that x = (2, 1, 0, 3), y = (8, —1, 5, 2). and z = (1, 0, 2, 1). Which of the following vectors

are in span {x, y, z} ?
(A) (2, 3, - 7, 3). (3) (1, 1, 1, 1).
(C) Both (A) and (B). (D) Neither (A) nor (B).
Which of the following is true ?
(ಗಿ) A finite set that contains 0 is linearly dependent.
(B) A set with exactly one vector is linearly independent if and only if that vector is not 0.

(C) A set with exactly two vectors is linearly independent if and only if neither vector is a

scalar multiple of the other.
(D) Allaretrue.
Which of the following sets of vectors in R3 are linearly independent.
(ಸಿ) {(2, 1, 2), (8, 4, 8).
(8) {(1, 1, 0), (1, 1, 1), (0, 1, -1)).
(C) (1, 3, 2), (1, - 7, - 8), (2, 1, -1)).

(10) {(-2, 0, 1), (3, 2, 5), (6, — 1, 1), (7, 0, -2)).

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