Question 7. Which of the following sets are a basis for the null space of 1-1...
_Determine which of these sets is a basis for R3. 1 - 1 ^ {[:] 7] [8]} - {[7] | c{[7] [8] [8]} » {[![10]} Determine the dimension of the subspace W = span {V1, V2, V3, V4} where A. dim(W)=1 B. dim(W) = 2 C. dim(W) = 3 D. dim(W) = 4 8 Determine both the rank and nullity of the matrix A= [1 0 1 | 2 -3 4 -2 -2 2 -4 1 0 3 -4 2...
1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2 1. Find a basis for the null space and row space of 1-13 (a) A 5-4 -4 7 -6 2 2 0 3 (b) A544 7 -6 2
QUESTION 9 [1200 Find a basis for the null space of A= 1 2 1 1 [ 1 200 O a.[-2 1 0 0 b. none of these 1 1 d. 0 -1 0 0 0 b. none of these का
(1 point) Find a basis for the column space, row space and null space of the matrix 8 -4 4 -2 6 2 -5 -4 1 -1 -3 2 -1 Basis of column space: {T Basis of row space: OTT {{ Basis of row space: Basis of null space:
(3) Determine which of the following sets is linearly independent. 02-1 (a) If the set is linearly dependent, express one vector as a non-zero linear combination of the other vectors in the set. (b) If the set is linearly independent, show that the only linear combination of the above vectors which gives the zero vector is such that all scalars are zero. (c) For each of the sets, determine if the span of the vectors is the whole space, a...
[1 3 0 3 Find a basis for the null space of A = 1 1 4 0 3 4 15
5. (a) (7 marks) Determine whether the following sets form a basis for R3. Explain your answers. i. - {0:0} - {0:00) - {000) -*-**(0-1 1 (b) (3 marks) Is the set W = a vector space? Explain your answer.
linear alegbra 7. Which set is not a subspace of R37 0 1 27 (A) null0 1 2 0 1 2] (B) span | |0| , |l | , | 2 (D) All of the given sets are subspaces of R3. 1 0 3 8. Which set is a basis for the null space of 2 -3 0 -1 2 1 (A)23 (B)01 3 2 3 (C)2 18
Q1. Find a basis and dimension for row space, column space and null space for the matrix, -2 - 4 A= 3 6 -2 - 4 4 5 -6 -4 4 9 (Marks: 6)
Find a basis for the null space of each matrix given 3 3 1 B= 0 2. N(B) = {1,62,bg} 1 2. 3. b_1 b_2 |b_3 - 2 -4 -3 C= -1 3 N(C) = {ci, C2, C3, C4 } -1 -1 3 -4, |c_1 c_2 C_3 |c_4