1 2 0 Let A = 12 1 0 h 1 a) For which hare the columns of A linearly dependent? b) For which h is the system Ax = 0 inconsistent? C) For which h do the columns of A span R 3? 2 d) For which h is the vector 4 in the span of the columns of A?

1 2 0 Let A = 12 1 0 h 1 a) For which hare the columns of A linearly dependent? b) For which h is the system Ax = 0 inconsistent? C) For which h do the columns of A span R 3? 2 d) For which h is the vector 4 in the span of the columns of A?

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

1 2 0
Let A = 1 2 1
0 h 1
a) For which h are the columns of A linearly dependent?
b) For which h is the system Ax = 0 inconsistent?
C) For which h do the columns of A span R 3?
2
d) For which h is the vector 4 in the span of the columns of A?
2

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