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. Use the rank nullity theorem to answer the following questions: (a) Suppose you have a...
Request for the answers with proofs for the below questions? I know for Answer to Question 2 is 1<=nullity(A)<=n....
Request for the answers with proofs for the below questions?
I know for Answer to Question 2 is 1<=nullity(A)<=n. But
not confident on the answer.
Question2 If Aisamx n matrix, what are the possible values of nullity(A)? (m-1) nullity A) nullitylA)Sn nullitylA)-O nullityA)2 m 4 Previous Question 3 For what values of "a does matrix 0 1 have rank 2? O a-3/2 a-2/5 uestion 4 et A be k x k matrix with real entries and x # 0. Then...
Please answer from part a through u The Fundamental Matrix Spaces: Consider the augmented matrix: 2...
Please answer from part a through u
The Fundamental Matrix Spaces: Consider the augmented matrix: 2 -3 -4 -9 -4 -5 6 7 6 -8 4 1 3 -2 -2 9 -5 -11 -17 -16 3 -2 -2 7 14 -7 2 7 8 12 [A[/] = 2 6 | -2 -4 -9 | -3 -3 -1 | -10 8 11 | 11 1 8 / 7 -10 31 -17 with rref R= [100 5 6 0 3 | 4...
What is the differance between these two questions and how I can defer between them to know which theorem I should use while solving question to find matrix A Theorem 2: lf S={5-s,, , s. and R={...
What is the differance between these two questions and how I
can defer between them to know which theorem I should use while
solving question to find matrix A
Theorem 2: lf S={5-s,, , s. and R={万佐, ,r;"} are ordered bases for vector spaces V and W respectively, then corresponding to each linear transformation L from V →W , there is an m x n matrix A such that for each ve V·A is the matrix representing L relative to...
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coum...
please provide detailed and clear solutions for the
following
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-e...
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your...
2. (a) Use Cramer's rule to solve for y and . (b) Let A be the augmented matrix representing the above system Based on your answer(s) to part (a), what is the dimension of the ullspace of A? (Not...
2. (a) Use Cramer's rule to solve for y and . (b) Let A be the augmented matrix representing the above system Based on your answer(s) to part (a), what is the dimension of the ullspace of A? (Note: Do NOT compute the basis. You MUST use the Equivalence Theorem and the answer to (a) and erplain how you know the answer.)
2. (a) Use Cramer's rule to solve for y and . (b) Let A be the augmented matrix...
2. Suppose that T: Rn → Rm is defined by T,(x)-A, x for each of the...
2. Suppose that T: Rn → Rm is defined by T,(x)-A, x for each of the matrices listed below. For each given matrix, answer the following questions: A, 0-10 0 0 0.5 A2 00 3 lo 3 0 For each matrix: R" with correct numbers for m and n filled in for each matrix. what is Rewrite T, : R, the domain of T? What is the codomain of T? a. Find some way to explain in words and/or graphically...
Due in 2 hr (a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the mat...
Due in 2 hr
(a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
please use octave calculator or matlab to answer (a)(ii)and(iii) 2. (a) Use Octave as a Calculator1 to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matri...
please use octave calculator or matlab to answer
(a)(ii)and(iii)
2. (a) Use Octave as a Calculator1 to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i, j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i, j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices...
Please show work/explain answer. Use the binomial theorem to expand (x + 2y)^5. You must illustrate...
Please show work/explain answer. Use the binomial theorem to expand (x + 2y)^5. You must illustrate use of the binomial theorem.
Request for the answers with proofs for the below questions?
I know for Answer to Question 2 is 1<=nullity(A)<=n. But
not confident on the answer.
Question2 If Aisamx n matrix, what are the possible values of nullity(A)? (m-1) nullity A) nullitylA)Sn nullitylA)-O nullityA)2 m 4 Previous Question 3 For what values of "a does matrix 0 1 have rank 2? O a-3/2 a-2/5 uestion 4 et A be k x k matrix with real entries and x # 0. Then...
Please answer from part a through u
The Fundamental Matrix Spaces: Consider the augmented matrix: 2 -3 -4 -9 -4 -5 6 7 6 -8 4 1 3 -2 -2 9 -5 -11 -17 -16 3 -2 -2 7 14 -7 2 7 8 12 [A[/] = 2 6 | -2 -4 -9 | -3 -3 -1 | -10 8 11 | 11 1 8 / 7 -10 31 -17 with rref R= [100 5 6 0 3 | 4...
What is the differance between these two questions and how I
can defer between them to know which theorem I should use while
solving question to find matrix A
Theorem 2: lf S={5-s,, , s. and R={万佐, ,r;"} are ordered bases for vector spaces V and W respectively, then corresponding to each linear transformation L from V →W , there is an m x n matrix A such that for each ve V·A is the matrix representing L relative to...
please provide detailed and clear solutions for the
following
2-6 3 2- 0 -103-5 Calculate the determinants of A and B -1 4 (use either appropriate row and coumn expansions or elementary row operations and the properties of determinants). Are A and B invertible? Calculate their inverses if they exist 1b. Are the columns of A linearly dependent or linearly independent? Find the dimension of Nul A and the rank of A. What can you say about the number of...
Suppose that 4 3 -225 3 3 -3 2 6 -2 -2 2-1 5 In the following questions you may use the fact that the matrix B is row-equivalent to A, where 1 0 1 0 1 0 1 -2 0 5 0 0 01 3 (a) Find: the rank of A the dimension of the nullspace of A (b) Find a basis for the nullspace of A. Enter each vector in the form [x1, x2, ...]; and enter your...
2. (a) Use Cramer's rule to solve for y and . (b) Let A be the augmented matrix representing the above system Based on your answer(s) to part (a), what is the dimension of the ullspace of A? (Note: Do NOT compute the basis. You MUST use the Equivalence Theorem and the answer to (a) and erplain how you know the answer.)
2. (a) Use Cramer's rule to solve for y and . (b) Let A be the augmented matrix...
2. Suppose that T: Rn → Rm is defined by T,(x)-A, x for each of the matrices listed below. For each given matrix, answer the following questions: A, 0-10 0 0 0.5 A2 00 3 lo 3 0 For each matrix: R" with correct numbers for m and n filled in for each matrix. what is Rewrite T, : R, the domain of T? What is the codomain of T? a. Find some way to explain in words and/or graphically...
Due in 2 hr
(a) Use Octave as a Calculator to answer this question Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i,j)-entry of the matrix A equals 0 if i +j is divisible by 5 and equals the (i,j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices A and B? Is vector u =[964,-71,4249, 59, 234,-196.97]...
please use octave calculator or matlab to answer
(a)(ii)and(iii)
2. (a) Use Octave as a Calculator1 to answer this question. Suppose that A and B are two 8 × 9 matrices. The (i, j)-entry of the matrix B is given by i *j -1. The (i, j)-entry of the matrix A equals 0 if i + j is divisible by 5 and equals the (i, j)-entry of the matrix B otherwise. i. What are the rank and nullity of matrices...
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