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f. If x₁ = (4,1,-1,1,0), then Ax₁ = g. If x₂ = (1, -2,-2,0, 1), then Ax₂ = Is X₁ in the null space of A? yes then Ax3 = . Is X₂ in the null space of A? yes h. If x3 = 3x2 - 4x₁ = Is X3 in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter al for a₁, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as comma separated list of vectors. A basis for the null space of A is { }

f. If x₁ = (4,1,-1,1,0), then Ax₁ = g. If x₂ = (1, -2,-2,0, 1), then Ax₂ = Is X₁ in the null space of A? yes then Ax3 = . Is X₂ in the null space of A? yes h. If x3 = 3x2 - 4x₁ = Is X3 in the null space of A? yes i. Find a basis for the null space of of A. If necessary, enter al for a₁, etc., or enter coordinate vectors of the form <1,2,3> or <1,2,3,4>. Enter your answer as comma separated list of vectors. A basis for the null space of A is { }

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 a5 are vectors in R³, A = (A₁ | A₂ | A3 | A | a5), and rref(A) = = 10 0 0 1 0 0011 -4 -1 2 2
Transcribed Image Text:Suppose a₁, A2, A3, a4, and a5 are vectors in R³, A = (A₁ | A₂ | A3 | A | a5), and rref(A) = = 10 0 0 1 0 0011 -4 -1 2 2
f. If x₁ = (4,1,-1,1,0), then Ax₁ g. If x₂ = (1,-2,-2, 0, 1), then Ax₂ = h. If X3 = = 3x₂ - 4x₁ = = . 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 { " then Ax3 . Is X₁ in the null space of A? yes Is X2 in the null space of A? yes =
Transcribed Image Text:f. If x₁ = (4,1,-1,1,0), then Ax₁ g. If x₂ = (1,-2,-2, 0, 1), then Ax₂ = h. If X3 = = 3x₂ - 4x₁ = = . 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 { " then Ax3 . Is X₁ in the null space of A? yes Is X2 in the null space of A? yes =
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