4. Answer each of the following for the given matrix and its reduced row echelon form:113 3 61 0 10 22-10-3 00 1 2 0 13 0 3 -1 5a. What is the rank of M?M =00 0b. What is the nullity of M?c. What is a basis for the Colsp (M)?1 1

Answered: Image /qna-images/answer/0e3b8eed-59d0-4c74-a5cb-73f501b07541.jpg

Answered: 4. Answer each of the following for the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. what is the rank of matrix A 2. Calculate the column space (aka range) of A 3.The nonzero row vectors of the above solution will give a basis for the column space of ?, denoted C(A). Write the column space of ? as a linear combination of these nonzero vectors:
3. Find an example of a matrix that has Why can't this be a basis for the row space and the mullspace? 1. Explain why the vector v = H and as a basis for its row space and its column space. cannot be a row of A and also in the nullspace of A.
Solve the following equation involving a determinant. If you have multiple answers, enter them as a list, separated by commas. 1 det( 2 = 38 x + 3 X =
IV. Let B₁ = {V₁, V2, V3} and B₂ = {w₁, w2, w3} be ordered bases of R³. The change of basis matrix from B₂ to B₁ is [213] P = 0 1 2 [103] 1. Write w₁ w₂ + 2w3 as a linear combination of v₁, U2, U3. 2. Determine P-1 using elementary row operations. 3. Suppose f: R³ R³ is the linear transformation such that f(v1) = 2v1 + v3, f(v2) = v2 +2v3, f(v3) = v₁ + 2v2. Find the matrix representation A off with respect to B₁. 4. What is the matrix representation C of f with respect to B₂?
Consider the following matrix A and its reduced row-echelon form: -3 12 -6 -27 -24 -2 -9 -8 −1 4 3 6 -24 -15 18 21 -1 0 0 3 4 3 A = 3 0 H 0 Dimension of null(A): 1 Find the dimensions of row(A), null(A), and col(A), and give a basis for each of them. Dimension of row(A): 1 Basis for row(A): Basis for null(A): 0 0 0 Dimension of col(A): 1 {}} Basis for col(A): rref(A) = 1 0 0 −3 −4 −3 01 -4 -1 5 5 000 0 00 000 0 0 0
4. Consider the following matrix A, where -2 4 -2 -4 A = 2 -6 -3 1 -3 8 2 -3 Find bases for and dimensions of Nul(A) and Col(A).
Find the transpose of the following: In all of the matrix calculations below, you must show your work! ⌈ 1 5 9 13 ⌉ | 2 4 10 14 | | 3 7 11 15 | ⌊ 4 8 12 16 ⌋ ⌈ 4 ⌉ | 3 | | 2 | ⌊ 1 ⌋
Suppose A, B, and X are invertible 3 x 3 matrices. Suppose that [1 2 0] 0 1 1 1 3 -1 1 • A-1 and B 2 3 1 1 0 • A8 = I3; and • 4A-((A²B)" X)" = (A²B)². T Find the matrix X.
Determine whether the following is a basis. 1. S %3 (4 - х, х3, бх?, х3 + 3х, 4х - 1} 01 [1 4 3. 2. 2. S = Note: after each matrix it has a comma.

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4. Answer each of the following for the given matrix and its reduced row echelon form: 1 1 3 3 6 10102 2 -1 0-3 0 :]-[ M = 3 0 3-15 a. What is the rank of M? 0 1 2 0 0 0 b. What is the nullity of M? c. What is a basis for the Colsp (M)? 0 1 1 1