True or False. 1. If S = {v1, v2, , Un}and S' = {wj,w2, ., wm} are any two bases of a subspace V of R0, then n must equal m. %3D 2. If 2 u +37 + 4w = 5 ủ + 67 +7w, then the vectors u, 3, wmust be linear independent. 3. {x, x², x }is a basis of P3. 4. {(1, 2), (4, –3), (2, 8)}form a basis of R2. 5. If the kernel of a matrix A consists of the zero vector only, then the column vectors of A must be linearly independent.
True or False. 1. If S = {v1, v2, , Un}and S' = {wj,w2, ., wm} are any two bases of a subspace V of R0, then n must equal m. %3D 2. If 2 u +37 + 4w = 5 ủ + 67 +7w, then the vectors u, 3, wmust be linear independent. 3. {x, x², x }is a basis of P3. 4. {(1, 2), (4, –3), (2, 8)}form a basis of R2. 5. If the kernel of a matrix A consists of the zero vector only, then the column vectors of A must be linearly independent.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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
Transcribed Image Text:True or False.
1. If S = {v, 02, .. , Un}and S' = {wi,w2,
.*, Wm}are any two bases of a subspace V of R10, then n must equal m.
2. If 2 u +3 + 4w = 5u + 6 ú +7u, then the vectors u, v, wmust be linear independent.
3. {x, x², x' }is a basis of P3.
4. {(1,2), (4, –3), (2, 8)}form a basis of R2.
5. If the kernel of a matrix A consists of the zero vector only, then the column vectors of A must be linearly independent.
6. The dimension of the vector space of all lower triangular 5 x 5matrices is 15.
7. There is a set of 6 linearly independent vectors that spans R'.
8. A basis for a n-dimensional vector space must have (n+1) vectors.
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