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Suppose a1, a2, a3, a4, and ag are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 -5 5 rref(A) 0 1 4 0 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1, az} = R³ MB. {a1, a2} is a linearly independent set OC. {a1, a2, a3, a4} is a basis for R3 OD. span{a1, a2, a3} = R3 VE. span{a1, a2, a3, a4} = R VF. {a1, a2, a3} is a linearly independent set OG. {a1, a2, a3, a4} is a linearly independent set OH. {a1, az} is a basis for R3 VI. {a1, a2, a3} is a basis for R3 b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = -5a1 + 4a2 + a3 c. The dimension of the column space of A is 3 and the column space of A is a subspace of R^3 d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { a1,a2,a3 e. The dimension of the null space of A is 2 and the null space of A is a subspace of R^5 f. If x1 = (5, –4, –1,1, 0), then Ax1 = [0,0,0] Is x1 in the null space of A? yes g. If x2 = (-5, -2, 3,0, 1), then Ax2 = [0,0,0] Is x2 in the null space of A? yes h. If x3 = 3x2 – 4x1 = [0,0,0] then Ax3 = Is xg in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter a1 for ai, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { [5,-4,-1,1,0],[-5,-2,3,0,1]

Suppose a1, a2, a3, a4, and ag are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 -5 5 rref(A) 0 1 4 0 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1, az} = R³ MB. {a1, a2} is a linearly independent set OC. {a1, a2, a3, a4} is a basis for R3 OD. span{a1, a2, a3} = R3 VE. span{a1, a2, a3, a4} = R VF. {a1, a2, a3} is a linearly independent set OG. {a1, a2, a3, a4} is a linearly independent set OH. {a1, az} is a basis for R3 VI. {a1, a2, a3} is a basis for R3 b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = -5a1 + 4a2 + a3 c. The dimension of the column space of A is 3 and the column space of A is a subspace of R^3 d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { a1,a2,a3 e. The dimension of the null space of A is 2 and the null space of A is a subspace of R^5 f. If x1 = (5, –4, –1,1, 0), then Ax1 = [0,0,0] Is x1 in the null space of A? yes g. If x2 = (-5, -2, 3,0, 1), then Ax2 = [0,0,0] Is x2 in the null space of A? yes h. If x3 = 3x2 – 4x1 = [0,0,0] then Ax3 = Is xg in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter a1 for ai, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { [5,-4,-1,1,0],[-5,-2,3,0,1]

Advanced Engineering Mathematics
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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Suppose a1, a2, a3, a4, and az are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 0 -5 1 0 5 rref(A) 4 [0 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1, a2} = R³ |B. {a1, a2} is a linearly independent set )C. {a1, a2, a3, a4} is a basis for R3 D. span{a1, a2, a3} = R³ E. span{a1, a2, a3, a4} = R³ F. {a1, a2, a3} is a linearly independent set |G. {a1, a2, a3, a4} is a linearly independent set |H. {a1, a2} is a basis for R3 V1. {a1, a2, a3} is a basis for R³ b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = -5а1 + 4а2 + а3 c. The dimension of the column space of A is 3 and the column space of A is a subspace of R^3 d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { a1,a2,a3 e. The dimension of the null space of A is 2 and the null space of A is a subspace of R^5 f. If x1 (5, –4, –1, 1,0), then Ax1 [0,0,0] Is x1 in the null space of A? yes g. If x2 = (-5, -2, 3,0, 1), then Ax2 = [0,0,0] Is x2 in the null space of A? yes h. If x3 Зx — 4х1 [0,0,0] then Ax3 Is x3 in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { [5,-4,-1,1,0],[-5,-2,3,0,1] }
Transcribed Image Text:Suppose a1, a2, a3, a4, and az are vectors in R³, A = (a1 | a2 | a3 | a4 | a5), and [1 0 0 -5 1 0 5 rref(A) 4 [0 0 1 1 -3 a. Select all of the true statements (there may be more than one correct answer). OA. span{a1, a2} = R³ |B. {a1, a2} is a linearly independent set )C. {a1, a2, a3, a4} is a basis for R3 D. span{a1, a2, a3} = R³ E. span{a1, a2, a3, a4} = R³ F. {a1, a2, a3} is a linearly independent set |G. {a1, a2, a3, a4} is a linearly independent set |H. {a1, a2} is a basis for R3 V1. {a1, a2, a3} is a basis for R³ b. If possible, write a4 as a linear combination of a1, a2, and a3; otherwise, enter DNE. a4 = -5а1 + 4а2 + а3 c. The dimension of the column space of A is 3 and the column space of A is a subspace of R^3 d. Find a basis for the column space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4,5>. Enter your answer as a comma separated list of vectors. A basis for the column space of A is { a1,a2,a3 e. The dimension of the null space of A is 2 and the null space of A is a subspace of R^5 f. If x1 (5, –4, –1, 1,0), then Ax1 [0,0,0] Is x1 in the null space of A? yes g. If x2 = (-5, -2, 3,0, 1), then Ax2 = [0,0,0] Is x2 in the null space of A? yes h. If x3 Зx — 4х1 [0,0,0] then Ax3 Is x3 in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter a1 for a1, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as a comma separated list of vectors. A basis for the null space of A is { [5,-4,-1,1,0],[-5,-2,3,0,1] }
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