![QUESTION 1 The columns of matrix B are given below. Which matrix B makes A similar to matrix D A = -8 -10] 15 17 B = {{3}{-1}](http://img.homeworklib.com/questions/6bf5ccf0-7052-11eb-9d05-d3dae8485f05.png?x-oss-process=image/resize,w_560)
Homework Answers
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QUESTION 1 The columns of matrix B are given below. Which matrix B makes A similar...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x)...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
please answer both questions thank you! How many rows and columns must a matrix A have...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
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...
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1....
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Linear Algebra Question: 18. Consider the system of equations Ax = b where | A= 1...
Linear Algebra Question:
18. Consider the system of equations Ax = b where | A= 1 -1 0 3 1 -2 -1 4 2 0 4 -1 –4 4 2 0 0 3 -2 2 2 and b = BENA 1 For each j, let a; denote the jth column of A. e) Let T : Ra → Rb be the linear transformation defined by T(x) = Ax. What are a and b? Find bases for the kernel and image...
Question 5 For each given vector b and matrix A, determine if b e im(A) 1...
Question 5 For each given vector b and matrix A, determine if b e im(A) 1 -2 3 (a) b 0 A 21 3 0 5 15 (b) b A2-24 9 Question 6 Find the rank and nullity of the given linear transformations T and determine which are one-to-one and which are onto. r+ y ri+r2 Question 7 Find nullity(T) if (a) T:R R2, rank(T) 1 (b) T:RR, rank(T) 0 (c) T : Rs ? R2, rank(T)-1 Question 8 Let...
18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h...
18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h 2 -3 k 4 a. What are the domain and codomain of T? b. Find the REF of [T]. Hint: You'll need the REF in some of the following questions. -1 -1 -1 -3 (REF of [7]= 0 2 2 4 is given here so that you can correctly answer the following 0 0 h – 2 k-6 questions.) c. Define the range of...
A.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero mat...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
For each transformation below, find the closed form of the transformation. 1) Let T be a...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...
Question 1.2 Let T : R3 ? R2 be a linear transformation given by T (x) = Ax, where 1 0 2 -1 1 5 1) Find a basis for the kernel of T. 2) Determine the dimension of the kernel of T 3) Find a basis for the image(range) of T. 4) Determine the dimension of the image(range) of T. 5) Determine if it is a surjection or injection or both. 2 6) Determine whether or not v |0|...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
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...
Recall that if T: R" R" is a linear transforrmation T(x) = [Tx, where [T is the transformation matrix, then 1. ker(T) null([T] (ker(T) is the kernel of T) 2. T is one-to-one exactly when ker(T) = {0 3. range of T subspace spanned by the columns of [T] col([T) 4. T is onto exactly when T(x) = [Tx = b is consistent for all b in R". 5. Also, T is onto exactly when range of T col([T]) =...
Linear Algebra Question:
18. Consider the system of equations Ax = b where | A= 1 -1 0 3 1 -2 -1 4 2 0 4 -1 –4 4 2 0 0 3 -2 2 2 and b = BENA 1 For each j, let a; denote the jth column of A. e) Let T : Ra → Rb be the linear transformation defined by T(x) = Ax. What are a and b? Find bases for the kernel and image...
Question 5 For each given vector b and matrix A, determine if b e im(A) 1 -2 3 (a) b 0 A 21 3 0 5 15 (b) b A2-24 9 Question 6 Find the rank and nullity of the given linear transformations T and determine which are one-to-one and which are onto. r+ y ri+r2 Question 7 Find nullity(T) if (a) T:R R2, rank(T) 1 (b) T:RR, rank(T) 0 (c) T : Rs ? R2, rank(T)-1 Question 8 Let...
18. Let T be the matrix transformation T -1 2 0 -1 2 2 -1 h 2 -3 k 4 a. What are the domain and codomain of T? b. Find the REF of [T]. Hint: You'll need the REF in some of the following questions. -1 -1 -1 -3 (REF of [7]= 0 2 2 4 is given here so that you can correctly answer the following 0 0 h – 2 k-6 questions.) c. Define the range of...
4. True/False.As always, give a brief explanation for your answer, if true, why true, or if false what would make it true, or a counterexample - 2 pts each: a. If Spanv v, V}) = Span({w,W)= W , then W is 2-dimensional. b. The kernel of a linear transformation T: R8 -R5 cannot be trivial c. If A is an invertible matrix, then A is diagonalizable 0, then A cannot be full-rank d. If det(A) e. If A is an...
For each transformation below, find the closed form of the transformation. 1) Let T be a linear transformation from R$ to M22 (R) [i Let B=1 0:00 [. :] [11] [12] [0 ] Let C= 12 41 -17 -5 65 -27 92 Let M = be the matrix transformation of T from basis B to C 17 58 -15 -51 81 The closed form of the transformation is Tb 3-1 2) Let T be a linear transformation from P3(R) to...
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