Answered: Let 1 4 1 0 -12 0 12 A 1 -4 -3 -8 3 4… | bartleby

Elementary Linear Algebra (MindTap Course List)

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.5: Basis And Dimension

Problem 66E

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Answer the boxes and highlight the answers thank you no ai generator

Let
1
4
1
0
-12
0
12
A
1
-4
-3 -8
3
4
-1 -8]
Find orthonormal bases of the kernel and column space of A.
Basis of the kernel:
Basis of the column space:
help (numbers)
help (numbers)
Book: Section A.5 of Notes on Diffy Qs

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A basis of {(a, b, c, d) : b = 6c+ d, a = 0} (A) {(0,0, 1,0), (0, 6, 0, 0), (0,0, 0, 1), (0, 1, 0, 0)} (B) {(0,1, 1,0), (0, 6, 0, 1)} (C) {(0,0, 1,0), (0, 6, 0, 0), (0, 1, 0, 1)} (D) {(0,6, 1,0), (0, 1, 0, 1)} (E) {(0,6, 1,0), (0, 6,0, 1)}
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Find a basis of the subspace of R* consisting of all vectors of the form x1 -9x1+ x2 -9x1– 2x2 -6x1+4x2] Your answer should be a list of row vectors separated by commas. (Click vector to learn about entering vectors.) Basis = {
n-{() ()}} - {}) 0 )} 12 2 3 B = 3 23 B2 1 3 21 2 2 {)0 ( B3 = B4 4 1 3 -2 a-{() 0} --{) 00} 3 2 B5 B6 = 1 1 2
Find an orthonormal basis for the space spanned by Calculator Check All Parts 4 - 2 and 2 201
tks~~
Let A = 0 -2 0 2 -3 -2 2 1 -4 2 -2 1 6 4 -3 -2 4 -2 2 a. A basis for the column space of A is { }. You should be able to explain and justify your answer. Enter a coordinate vector, such as or , or a comma separated list of coordinate vectors, such as , or ,. b. The dimension of the column space of A is answer): A. rref(A) has a pivot in every row. B. The basis we found for the column space of A has three vectors. OC. Three of the five columns in rref(A) have pivots. OD. Two of the five columns in rref(A) have pivots. □ E. rref(A) has a pivot in every column. □ F. rref(A) is the identity matrix. c. The column space of A is a subspace of d. The geometry of the column space of A is the origin inside R^5 because (select all correct answers -- there may be more than one correct because each column vector in A is a vector in R^4
b) Find the value of k such that (-1,1,1), (1,1,1), (1, -1, k) form a basis of R²

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