= 5. Consider the 4 x 5 matrix A = [u₁|u2|u3|us| us], where the columns are U₂ = Uz = A U4 = 8 -1 1 U5 = 1 a) Find a set of vectors in {u₁, U2, U3, us, us) which is a basis of the column space of A. b) Find the rank of A. D o
= 5. Consider the 4 x 5 matrix A = [u₁|u2|u3|us| us], where the columns are U₂ = Uz = A U4 = 8 -1 1 U5 = 1 a) Find a set of vectors in {u₁, U2, U3, us, us) which is a basis of the column space of A. b) Find the rank of A. D o
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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Question
![5. Consider the 4 × 5 matrix \( A = [ u_1 \, | \, u_2 \, | \, u_3 \, | \, u_4 \, | \, u_5 ] \), where the columns are
\[
u_1 = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}, \quad u_2 = \begin{bmatrix} 5 \\ 1 \\ 0 \\ 2 \end{bmatrix}, \quad u_3 = \begin{bmatrix} -2 \\ -2 \\ 1 \\ 3 \end{bmatrix}, \quad u_4 = \begin{bmatrix} 1 \\ 0 \\ -1 \\ 1 \end{bmatrix}, \quad u_5 = \begin{bmatrix} 1 \\ 2 \\ 2 \\ 5 \end{bmatrix}
\]
a) Find a set of vectors in \(\{u_1, u_2, u_3, u_4, u_5\}\) which is a basis of the column space of \( A \).
b) Find the rank of \( A \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff6c1c23e-1f73-4b65-bca5-bb8e7ffd22c6%2F1ac5ae4d-eaf2-4b41-ac50-478cb5f62056%2F41u47wd_processed.png&w=3840&q=75)
Transcribed Image Text:5. Consider the 4 × 5 matrix \( A = [ u_1 \, | \, u_2 \, | \, u_3 \, | \, u_4 \, | \, u_5 ] \), where the columns are
\[
u_1 = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}, \quad u_2 = \begin{bmatrix} 5 \\ 1 \\ 0 \\ 2 \end{bmatrix}, \quad u_3 = \begin{bmatrix} -2 \\ -2 \\ 1 \\ 3 \end{bmatrix}, \quad u_4 = \begin{bmatrix} 1 \\ 0 \\ -1 \\ 1 \end{bmatrix}, \quad u_5 = \begin{bmatrix} 1 \\ 2 \\ 2 \\ 5 \end{bmatrix}
\]
a) Find a set of vectors in \(\{u_1, u_2, u_3, u_4, u_5\}\) which is a basis of the column space of \( A \).
b) Find the rank of \( A \).
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