Determine whether the statement below is true or false. Justify the answer. If x and y are linearly independent, and if {x, y, z) is linearly dependent, then z is in Span{x, y). Choose the correct answer below. O A. The statement is true. If {x, y, z) is linearly dependent, then z must be a linear combination of x and y because x and y are linearly independent. So z is in Span(x, y). O B. The statement is false. If x and y are linearly independent, and {x, y, z) is linearly dependent, then z must be the zero vector. So z cannot be in Span{x, y). O C. The statement is true. If {x, y, z) is linearly dependent and x and y are linearly independent, then z must be the zero vector. So z is in Span{x, y). O D. The statement is false. Vector z cannot be in Span{x, y) because x and y are linearly independent.
Determine whether the statement below is true or false. Justify the answer. If x and y are linearly independent, and if {x, y, z) is linearly dependent, then z is in Span{x, y). Choose the correct answer below. O A. The statement is true. If {x, y, z) is linearly dependent, then z must be a linear combination of x and y because x and y are linearly independent. So z is in Span(x, y). O B. The statement is false. If x and y are linearly independent, and {x, y, z) is linearly dependent, then z must be the zero vector. So z cannot be in Span{x, y). O C. The statement is true. If {x, y, z) is linearly dependent and x and y are linearly independent, then z must be the zero vector. So z is in Span{x, y). O D. The statement is false. Vector z cannot be in Span{x, y) because x and y are linearly independent.
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:Determine whether the statement below is true or false. Justify the answer.
If x and y are linearly independent, and if {x, y, z) is linearly dependent, then z is in Span{x, y).
Choose the correct answer below.
O A. The statement is true. If {x, y, z) is linearly dependent, then z must be a linear combination of x and y because x and y are linearly
independent. So z is in Span(x, y).
O B.
The statement is false. If x and y are linearly independent, and {x, y, z) is linearly dependent, then z must be the zero vector. So z
cannot be in Span{x, y).
O C. The statement is true. If {x, y, z) is linearly dependent and x and y are linearly independent, then z must be the zero vector. So z is
in Span{x, y).
O D. The statement is false. Vector z cannot be in Span{x, y) because x and y are linearly independent.
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