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Question 1 Use the function ?(v . v,. v.) = (2v, +v,. v -v,) to find the preimage of W = (-1, 3) O a. N N 3 : .) where t is any real number O b. 7 2 3 ' 3 -. 4 .I; where t is any real number O d. 2 7 3 3 1, Where : is any real number 3 4Question 2 5x - 2y = 7 Use Cramer's Rule to solve the system of equations 2x - y = 1 O a. x=4, y = 8 O b. x = 5,y=9 Ocx= 5, V= $ O d.x= 7,y=7 O e. x = 9. y= 5Question 3 Sketch the image of the unit square with vertices at (0, 0), (1, 0), (1, 1), and (0, 1) under the transformation / which is the contraction given by 7(x, y) = (x + 2y, y)- O a (-3, 1) (0, 1 -1 - Ob (-3, 1) (-2, 1) -1 DC 3 (1, 3) (1, 2)O d. 3 24 (2, 1) (3, 1) 1 - -1 Oe 3 24 (0, 1) (3, 1)Question 4 8 16 3 Find a basis for the row space of a matrix 8 24 8 8 8 -2 0 8. ( 2, 0. 7 ) (0.2. ) (0.6. 14] D D. ( 2. 0. - 7). (0.2. 2 ))Question 5 Describe the zero vector (the additive identity) of the vector space P. O a. O(x) = 0x5 + 0x4+0x3+0x2+0x+0=0 O b. O(x) = 0x 3+0x2+ 0x+0=0 O c. O(x) = 0x4+ 0x3+0x2+0x+0=0 O d. O(x) = 0x + 0x5+ 0x4+0x3+0x2+0x+0=0 O e. O(x) = 0x2+0x+0 =0Question 6 The linear transformation 7: R- R' is defined by /(x) = Ax, where 9 A 12 0 15] Find range(D). O a {(r. 5r) | r ER) O b. {(5r, r) | PER) O c((r, 37) | PER] O d. R' De {(r, 0) |rER}Question 7 Find the kernel of the linear transformation 7: R- - R', defined by (x, y) = (2x + By. 6y -2x). O a. ker(D) = ((r, P) | PER) O b. ker(7) = ((s, 25) | s ER} O c ker(D) = ((s, 35) |s ER} O d. ker(D) = {(1, 1+ 1) |rER} O e. ker(7) = {(0. 0)}Question 8 Explain why $ = -.:is not a basis for My. O a. none of these choices O b. S is linearly dependent and spans M22. O c. S is linearly independent and spans Maz. O d. S is linearly independent and does not span Man. O e. S is linearly dependent and does not span M22-Question 9 7 12 1 2 Which property of determinants is illustrated by the equation 2 9 2 =- 38 8 ? 3 8 8 292 O a. If a column of a matrix is subtracted from another column, the determinant of the matrix is multiplied by -1. O b. If a row of a matrix is subtracted from another row of the same matrix, the determinant of the matrix is multiplied by -1. O c. If two rows of a matrix are interchanged, the determinant of the matrix is multiplied by -1. O d. If two columns of a matrix are interchanged, the determinant of the matrix is multiplied by -1. O e. If two matrices have any rows equal, the determinant of the matrix is multiplied by -1.Question 10 True or false. The set S = {(-1, 4). (2. -8)} spans R-. O True O FalseQuestion 11 Let 7: R" - R' be a linear transformation. Find the nullity of / given that rank(7) = 5- O a. nullity(T) = 4 O b. nullity(7) = 6 O c. nullity(7) = 14 O d. nullity(7) = 5 O e. nullity(7) = 16