Problem 1: Determine whether the following sets form subspaces of R². a. {(X1, X2)T|X1 + X2 = 0} -> is a subspace of R² b. {(x1, x2)T|X1 X2 = 0} -> is not a subspace of R² C. {(x1, x2) T|X1 = 3x2} -> is a subspace of R² d. {(x1, x2)T||X1| = |x2|} -> is not a subspace of R² e. {(x1, x2) ¹|x²1= x²2} -> is not a subspace of R²

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Problem 1:
Determine whether the following sets form subspaces of R².
a. {(X1, X2)T|X1 + X2 = 0} -> is a subspace of R²
b. {(x1, x2)T|X1 X2 = 0} -> is not a subspace of R²
C. {(x1, x2) T|X1 = 3x2} -> is a subspace of R²
d. {(x1, x2)T||X1| = |x2|} -> is not a subspace of R²
e. {(x1, x2) ¹|x²1= x²2} -> is not a subspace of R²
Transcribed Image Text:Problem 1: Determine whether the following sets form subspaces of R². a. {(X1, X2)T|X1 + X2 = 0} -> is a subspace of R² b. {(x1, x2)T|X1 X2 = 0} -> is not a subspace of R² C. {(x1, x2) T|X1 = 3x2} -> is a subspace of R² d. {(x1, x2)T||X1| = |x2|} -> is not a subspace of R² e. {(x1, x2) ¹|x²1= x²2} -> is not a subspace of R²
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