Holt Mcdougal Larson Pre-algebra: Student Edition 2012
1st Edition
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
Chapter1: Variables, Expressions, And Integers
Section: Chapter Questions
Problem 17CR
Related questions
Question
Explain why S is not a basis for M2,2.
Expert Solution
Step 1
Let's check if S is linearly independent or not.
S will not be linearly independent if for some constant a, b, c & d we are able to show:
Step 2
Hence,
a - c = 0
a + b = 0
b + c = 0
d = 0
Let's say a = x, then b = -a = -x; c = a = x, d = 0
Hence, (x, -x, x, 0) is one such solution.
Since x is any arbitrary value, there exists and infinite number of solutions.
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