Homework Answers
![0-3 1 Therefore, the row space has a basis is as follows (2 4 6 8],[0 1 -3 1] The range space has a basis is as follows 21 [4](http://img.homeworklib.com/images/c2d24d15-0ed1-42a8-9e74-907c0eb6232f.latex?%5Cdpi%7B100%7D%20%5Csmall%20%7B%5Ccolor%7BRed%7D%20%28b%29%7D%5C%5C%20%5Csim%20%5Cbegin%7Bbmatrix%7D2%264%266%268%5C%5C%200%261%26-3%261%5C%5C%200%260%260%260%5Cend%7Bbmatrix%7D%5C%5C%20%5Ctextbf%7BTherefore%2C%20the%20row%20space%20has%20a%20basis%20is%20as%20follows%7D%5C%5C%20%5Cleft%20%5C%7B%20%5Cbegin%7Bbmatrix%7D2%264%266%268%20%5Cend%7Bbmatrix%7D%2C%5Cbegin%7Bbmatrix%7D%200%261%26-3%261%5Cend%7Bbmatrix%7D%20%5Cright%20%5C%7D%5C%5C%20%7B%5Ccolor%7BRed%7D%20%28c%29%7D%5C%5C%20%5Ctextbf%7BThe%20range%20space%20has%20a%20basis%20is%20as%20follows%7D%5C%5C%20%5Cleft%20%5C%7B%20%5Cbegin%7Bbmatrix%7D%202%5C%5C%200%5C%5C%200%20%5Cend%7Bbmatrix%7D%2C%5Cbegin%7Bbmatrix%7D%204%5C%5C%201%5C%5C%200%20%5Cend%7Bbmatrix%7D%20%5Cright%20%5C%7D%5C%5C?x-oss-process=image/resize,w_560)
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Problem 2 [2 4 6 81 Let A 1 3 0 5; L1 1 6 3 a) Find a basis for the nullspace of A b) Find the basis for the rowspace of A c) Find the basis for the range of A that consists of column vectors of...
For the following matrix: [1 1 2] |1 1 2| = A [2 3 5] a)...
For the following matrix: [1 1 2] |1 1 2| = A [2 3 5] a) Find a matrix B in reduced echelon form such that B is row equivalent to the given matrix A. b) Find a basis for the nullspace of A. c) Find a basis for the range of A that consists of columns of A. For each column, Aj, of A that does not appear in the basis, express Aj as a linear combination of the...
(1 point) Let A-0 -2 3 Find a basis of nullspace(A). Answer: To enter a basis...
(1 point) Let A-0 -2 3 Find a basis of nullspace(A). Answer: To enter a basis into WeBWorK, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 21 , then you would enter [1,2,3],11,1,1] into the answer blank.
3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis...
3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis for the nullspace of (b) 4 points] Using the columns of A, find a basis for the column space of A (c) [2 points What are the dimensions of these spaces? (d) [2 points] ls the vector u-I1-1 0 ојт in the nullspace of A? Why? (e) [4 points] Is the vector w-17-9 9-9]T İn the column space of A? If so, express w...
Please show work Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 =...
Please show work
Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
Problem 2. Let 1 1 1 3 1 2 1 1 6 1 A = 3...
Problem 2. Let 1 1 1 3 1 2 1 1 6 1 A = 3 1 1 9 1 4 1 1 12 1 (a): (7 points) Find a basis for rowspace(A) (b): (7 points) Find a basis for nullspace(A) (c): (4 points) Using (a)-(b), verify the Rank-Nullity Theorem for the matrix A above
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the r...
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the range of T.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for...
0 1 Let S span 1 1 1 0 }, a basis for S. Show that| (a) Let B1 { 1 0 1 1 0 is also a basis for S 0 B2 { 1 (b) Write eac...
0 1 Let S span 1 1 1 0 }, a basis for S. Show that| (a) Let B1 { 1 0 1 1 0 is also a basis for S 0 B2 { 1 (b) Write each vector in B2 (c) Use the previous part to write each vector in B2 with respect to Bi (how many components should each vB, vector have?) (d) Use the previous part to find a change of basis matrix B2 to B1. What...
Linear Algebra 6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2...
Linear Algebra
6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2 = (-2,3,1,0), V3 =(4,-5, 9,4), V4 = (0,4,2, -3) V5 = (-7, 18, 2, -8) that forms a basis for the space spanned by these vectors. (b) Use (a) to express each vector not in the basis as a linear combination of the basis vectors. (c) Let Vi V2 A= V3 V4 Use (a) to find the dimension of row(A), col(A), null(A), and of...
(1 point) Let A = 2 2 | -4 1-2 6 -3 -3 3 3 -3...
(1 point) Let A = 2 2 | -4 1-2 6 -3 -3 3 3 -3 0 3 4 7 1 -5 -1 Find a basis of nullspace(A). Answer: [1,0,3/2,0], [0,-3/9,0,1] To enter a basis into WeBWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 12, 1 }, then you would enter [1,2,3],[1,1,1) into the answer blank. U 3 ||1
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find...
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find bases for the four fundamental subspaces of the matrix A. Basis for n(A) = nullspace of A: Basis for N(4")= nullspace of A": Basis for col(A) = column space of A: Basis for col(A) = column space of A': () Give a vector space that is isomorphic to col (A) N(A).
(1 point) Let A-0 -2 3 Find a basis of nullspace(A). Answer: To enter a basis into WeBWorK, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 21 , then you would enter [1,2,3],11,1,1] into the answer blank.
3. You are given the following matrix -4 12 2 7 a)4 points) Find a basis for the nullspace of (b) 4 points] Using the columns of A, find a basis for the column space of A (c) [2 points What are the dimensions of these spaces? (d) [2 points] ls the vector u-I1-1 0 ојт in the nullspace of A? Why? (e) [4 points] Is the vector w-17-9 9-9]T İn the column space of A? If so, express w...
Please show work
Problem 2. Consider the vectors [1] 1 1 v1 = 1, V2 = -1, V3 = -3 , 04 = , 05 = 6 Let S CR5 be defined by S = span(V1, V2, V3, V4, 05). A. Find a basis for S. What is the dimension of S? B. For each of the vectors V1, V2, V3, V4.05 which is not in the basis, express that vector as linear combination of the basis vectors. C. Consider...
Problem 2. Let 1 1 1 3 1 2 1 1 6 1 A = 3 1 1 9 1 4 1 1 12 1 (a): (7 points) Find a basis for rowspace(A) (b): (7 points) Find a basis for nullspace(A) (c): (4 points) Using (a)-(b), verify the Rank-Nullity Theorem for the matrix A above
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for the nullspace (Kernel) of T. c) Find a basis for the range of T.
7.) 10points Let V be the space of 2 x 2 matrices. Let T: V-V be given by T(A) = A a.) Prove that T a linear transformation b.) Find a basis for...
0 1 Let S span 1 1 1 0 }, a basis for S. Show that| (a) Let B1 { 1 0 1 1 0 is also a basis for S 0 B2 { 1 (b) Write each vector in B2 (c) Use the previous part to write each vector in B2 with respect to Bi (how many components should each vB, vector have?) (d) Use the previous part to find a change of basis matrix B2 to B1. What...
Linear Algebra
6. (8pt) (a) Find a subset of the vectors v1 = (1, -1,5,2), V2 = (-2,3,1,0), V3 =(4,-5, 9,4), V4 = (0,4,2, -3) V5 = (-7, 18, 2, -8) that forms a basis for the space spanned by these vectors. (b) Use (a) to express each vector not in the basis as a linear combination of the basis vectors. (c) Let Vi V2 A= V3 V4 Use (a) to find the dimension of row(A), col(A), null(A), and of...
(1 point) Let A = 2 2 | -4 1-2 6 -3 -3 3 3 -3 0 3 4 7 1 -5 -1 Find a basis of nullspace(A). Answer: [1,0,3/2,0], [0,-3/9,0,1] To enter a basis into WeBWork, place the entries of each vector inside of brackets, and enter a list of these vectors, separated by commas. For instance, if your basis is 12, 1 }, then you would enter [1,2,3],[1,1,1) into the answer blank. U 3 ||1
1 4 2 1 7.[12pts) Let A = 0 1 1-2 -8 -4 -2 (a) Find bases for the four fundamental subspaces of the matrix A. Basis for n(A) = nullspace of A: Basis for N(4")= nullspace of A": Basis for col(A) = column space of A: Basis for col(A) = column space of A': () Give a vector space that is isomorphic to col (A) N(A).
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