Problem 1. Matrices and vector spaces. (a) Let A be an m x n matrix. Show that the null space of A is a linear subspace of R". Consider the 3 × 4 matrix 6. -4 2 A = 3 1 2 -3 2 22 -20 14 (b) Find a basis for the null space of A. (c) Find a basis for the column space of A. (d) Suppose that B is a 3 x 5 matrix and that the column space has dimen- sion 2. What is the dimension of the nullspace of B?
Problem 1. Matrices and vector spaces. (a) Let A be an m x n matrix. Show that the null space of A is a linear subspace of R". Consider the 3 × 4 matrix 6. -4 2 A = 3 1 2 -3 2 22 -20 14 (b) Find a basis for the null space of A. (c) Find a basis for the column space of A. (d) Suppose that B is a 3 x 5 matrix and that the column space has dimen- sion 2. What is the dimension of the nullspace of B?
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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Transcribed Image Text:Problem 1. Matrices and vector spaces.
(a) Let A be an m x n matrix. Show that the null space of A is a linear
subspace of R".
Consider the 3 × 4 matrix
-4
2
A =
3
1
2 -3
2 22 -20
14
(b) Find a basis for the null space of A.
(c) Find a basis for the column space of A.
(d) Suppose that B is a 3 x 5 matrix and that the column space has dimen-
sion 2. What is the dimension of the nullspace of B?
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