Suppose a1, az, az, a4, and ag are vectors in R', A = (a1 | a2 | a3 | a4 | a5), and[1 0 0 -5 4]1 0 -2 20 0 1rref(A) :1 d. Find a basis for the column space of of A. If necessary, enter a1 for a,, 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 {e. The dimension of the null space of A isand the null space of A is a subspace off. If x1 = (5, 2, –1,1,0), then Ax =Is x1 in the null space of A? chooseg. If x2 = (-4, -2, –1,0, 1), then Ax2 =s X, in the null space of A? choose vh. If X3 = 3x2 – 4x1 =then Ax3Is X3 in the null space of A? choose vi. Find a basis for the null space of of A. If necessary, enter a1 for a,. 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 {}

Given: The row reduction equivalence form of the matrix A is 100-54010-2200111. Explanation: d. The…

d. Find a basis for the column space of of A. If necessary, enter a1 for a, 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 { } e. The dimension of the null space of A is , and the null space of A is a subspace of f. If x1 = (5, 2, –1, 1,0), then Ax1 = .Is x1 in the null space of A? choose v g. If x2 = (-4, –2, –1,0, 1), then Ax2 = Is x2 in the null space of A? choose v h. If xg = 3x2 – 4x1 = , then Axg = Is xg in the null space of A? choose v

d. Find a basis for the column space of of A. If necessary, enter a1 for a, 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 { } e. The dimension of the null space of A is , and the null space of A is a subspace of f. If x1 = (5, 2, –1, 1,0), then Ax1 = .Is x1 in the null space of A? choose v g. If x2 = (-4, –2, –1,0, 1), then Ax2 = Is x2 in the null space of A? choose v h. If xg = 3x2 – 4x1 = , then Axg = Is xg in the null space of A? choose v

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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Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

Suppose a1, az, az, a4, and ag are vectors in R', A = (a1 | a2 | a3 | a4 | a5), and
[1 0 0 -5 4]
1 0 -2 2
0 0 1
rref(A) :
1

d. Find a basis for the column space of of A. If necessary, enter a1 for a,, 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 {
e. The dimension of the null space of A is
and the null space of A is a subspace of
f. If x1 = (5, 2, –1,1,0), then Ax =
Is x1 in the null space of A? choose
g. If x2 = (-4, -2, –1,0, 1), then Ax2 =
s X, in the null space of A? choose v
h. If X3 = 3x2 – 4x1 =
then Ax3
Is X3 in the null space of A? choose v
i. Find a basis for the null space of of A. If necessary, enter a1 for a,. 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 {
}

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