CCI Linear Algebra Assignment 2 1 Assignment 2 Due Date: 20 October 2015 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Determine whether the statement is true or false: 1. Vectors ( 7,0,2 ) , ( 4,9,14 ) are orthogonal to each other. 2. R2 is a subspaceR3 . 3. All linearly independent set in a subspace W is a basis for W . 4. The transformation 2 T :R R 2 , T ( x , y)=2 x +3 y is a linear transformation. 5. The column space of a 5 7 matrix is in R5 . 6. If A is m n matrix then row space of A and column space of A have different dimension. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - For Each Question, Choose the Correct Answer from the Multiple-Choice List. 1. If u=(5,1,4) and v =(1,0,2) are two vectors in the cross product u v : a. (5,0,8) b. (4,2,6) c. (2,14, 1) d. (0,0,0) R 3 . Then 2 2. Let T 1 ( v1 , v 2 )= ( v 1v 2 , v 1+ v 2 ) and value of T 1 (T 2 ( v 1 , v 2 )) is: a. (2 v 2 +2 v 1 ,2 v 12 v 2) b. ( 2 v 22 v 1 , 2 v 1+ 2 v 2) c. ( 2 v 12 v 2 , 2 v 1+ 2 v 2) d. ( 2 v 1 +2 v 1 ,2 v 12 v 2) T 2 ( v1 , v 2 ) =( 2 v 2 ,2 v 1 ) . The 3. Let S={v 1 , v 2 , v 3 } is a basis of V and v 2=3 v 15 v 2 . Then (v ) the coordinate vector of V relative to S s is: a. b. c. d. (3,5,0) (3,0,5) (5,3) (3,5) A linear combination formed by the vectors w 2=( 0,1,2 ) and w 3=( 2,0,4 ) is: 4. a. b. c. d. w 1=( 1,1,0 ) w 3=4 w13 w 2 w 2=w1 + w3 w 3=2 w12 w 2 w 1=w2w3 Solve the following questions: 1. If u=(6,2,3) and the angle between . Find and v . v =(1,1,1) u cos , where is , CCI Linear Algebra Assignment 2 {[ ] | } a+2 b W= 5b , a,b R 7 a+b 2. Let W 3. If 3 be a subset R3 . Find a basis for . 2u 1 , 2 u2 , 2 u1 +2u 2 T ( u1 , u2 )= ) is a transformation, find the domain, codomain and the image of ( 1,3 ) under T . 4. Given the 3 4 matrix. Find the basis for Row space of A and its dimension. Where A = [ 1 4 5 2 2 1 3 0 1 3 2 2