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Question 4 Choose the right answer out of a, b, or c for each problem (1) The vectors: a = [1; 0; 2], b = [0; -1; 1], c = [1; 1; 1] and d = [2; 0; 6] are given. (a) Vectors a, b, and c span R^3 (b) Vectors a, b, and c do not span R^3, but they span vector d (c) Vectors a, b, and c span a 2-dimensional subspace R^3 (2) a, b, and c are vectors. Then the expression a x c + b x a is (a) Meaningless (b) A vector collinear with a (c) A vector orthogonal to a (3) Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that ||a + b|| = ||a - b||. Then it follows that (a) b = 0 (b) a and b are proportional to each other (c) a and b are orthogonal (4) If A and B are square matrices of the same size and each of them is invertible, then (a) Matrix BA is invertible (b) AC = BC for any matrix C of the same size as A and B (c) None of the above is true

          Question 4 Choose the right answer out of a, b, or c for each problem

(1) The vectors: a = [1; 0; 2], b = [0; -1; 1], c = [1; 1; 1] and d = [2; 0; 6] are given.
(a) Vectors a, b, and c span R^3
(b) Vectors a, b, and c do not span R^3, but they span vector d
(c) Vectors a, b, and c span a 2-dimensional subspace R^3

(2) a, b, and c are vectors. Then the expression a x c + b x a is
(a) Meaningless
(b) A vector collinear with a
(c) A vector orthogonal to a

(3) Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that ||a + b|| = ||a - b||. Then it follows that
(a) b = 0
(b) a and b are proportional to each other
(c) a and b are orthogonal

(4) If A and B are square matrices of the same size and each of them is invertible, then
(a) Matrix BA is invertible
(b) AC = BC for any matrix C of the same size as A and B
(c) None of the above is true

Question 4 Choose the right answer out of a, b, or c for each problem

(1) The vectors: a = [1; 0; 2], b = [0; -1; 1], c = [1; 1; 1] and d = [2; 0; 6] are given.
(a) Vectors a, b, and c span R^3
(b) Vectors a, b, and c do not span R^3, but they span vector d
(c) Vectors a, b, and c span a 2-dimensional subspace R^3

(2) a, b, and c are vectors. Then the expression a x c + b x a is
(a) Meaningless
(b) A vector collinear with a
(c) A vector orthogonal to a

(3) Vectors a and b are some vectors in a space with inner Euclidean product, and it is known that ||a + b|| = ||a - b||. Then it follows that
(a) b = 0
(b) a and b are proportional to each other
(c) a and b are orthogonal

(4) If A and B are square matrices of the same size and each of them is invertible, then
(a) Matrix BA is invertible
(b) AC = BC for any matrix C of the same size as A and B
(c) None of the above is true

Added by Samantha W.

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