Homework Sets HW6 Problem 9 User Settings Grades Problems HW6: Problem 9 Previous Problem Problem List Next Problem (1 point) Let Problem 1 Problem 2 Problem 3 Problem 4 A basis for the column space of A is {\\ Problem 5 Problem 6 Preview My Answers Submit Answers Problem 7 Problem 8 Problem 9 You have attempted this problem 0 times. You have unlimited attempts remaining. Problem 10 Problem 11 Email instructor Problem 12 Problem 13 Problem 14 Problem 15 Problem 16 \begin{bmatrix} -2 & 4 & -4 & -1 & 0\\ -1 & 0 & 0 & 2 & 4\\ 4 & -4 & 5 & -3 & -8\\ -4 & 4 & -5 & 3 & 8 \end{bmatrix}.}
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In other words, it is the set of all possible linear combinations of the column vectors of A. To find a basis for the column space of A, we need to find a set of linearly independent column vectors of A that span the column space. Show more…
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Let A be a matrix with a basis for the column space of A. You should be able to explain and justify your answer. Enter a coordinate vector, such as <1,2,3,4> or <1,2,3,4,5>, or a comma-separated list of coordinate vectors, such as <1,2,3,4>,<5,6,7,8> or <1,2,3,4,5>,<6,7,8,9,10>. The dimension of the column space of A is because (select all correct answers -- there may be more than one correct answer): A. Two of the five columns in rref(A) have pivots. B. rref(A) is the identity matrix. C. rref(A) has a pivot in every column. D. rref(A) has a pivot in every row. E. Three of the five columns in rref(A) have pivots. F. The basis we found for the column space of A has three vectors. The column space of A is a subspace of because choose. The geometry of the column space of A is choose.
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2. Given A = [1 -2 1 1 3; -2 4 1 10 -3; -1 2 2 11 0] a) Find a basis for row space of A b) Find a basis for column space of A Note: you must use alternate technique discussed in class Step 1: reduce A→B Step 2: Take columns in A that correspond to identity elements in B c) Find rank(A) d) Find basis for nullspace(A) e) Find nullity(A)
Adi S.
1. Use the fact that matrices A and B are row-equivalent. A = −2 −5 8 0 −17 1 3 −5 1 5 3 11 −19 7 1 1 7 −13 5 −3 B = 1 0 1 0 1 0 1 −2 0 3 0 0 0 1 −5 0 0 0 0 0 (a) Find the rank and nullity of A. (b) Find a basis for the nullspace of A. (c) Find a basis for the row space of A. (d) Find a basis for the column space of A.
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