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a b -10 Let W = = € M₁x1 a, b, c, d = R, a + 4b - 3c = 0, and b+2c-d = 0) : (a) Show that every vector in W is of the form (c) Show that -4b+ 3c] b с b +2c A (10) 2 (b) Use (a) to conclude that W = span 2 is a basis for W. where b, c E R.

a b -10 Let W = = € M₁x1 a, b, c, d = R, a + 4b - 3c = 0, and b+2c-d = 0) : (a) Show that every vector in W is of the form (c) Show that -4b+ 3c] b с b +2c A (10) 2 (b) Use (a) to conclude that W = span 2 is a basis for W. where b, c E R.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.2: Linear Independence, Basis, And Dimension
Problem 33EQ
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Let W = a b € M4x1 a, b, c, d € R, a + 4b - 3c = 0, and b +2cd=0 d (a) Show that every vector in W is of the form (b) Use (a) to conclude that W = span (c) Show that -4b + 3c] b C b +2c D (10) 3 2 U 0 1 2 is a basis for W. where b, c E R.
Transcribed Image Text:Let W = a b € M4x1 a, b, c, d € R, a + 4b - 3c = 0, and b +2cd=0 d (a) Show that every vector in W is of the form (b) Use (a) to conclude that W = span (c) Show that -4b + 3c] b C b +2c D (10) 3 2 U 0 1 2 is a basis for W. where b, c E R.
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