(e) A set of vectors 0, vi,- uk is always linearly independent. (f) A basis for R³ can consist of 2 vectors. (g) (AT)T = A. (h) The rank of a 2 x 2 matrix 2 is 2. T F T F T F T F
(e) A set of vectors 0, vi,- uk is always linearly independent. (f) A basis for R³ can consist of 2 vectors. (g) (AT)T = A. (h) The rank of a 2 x 2 matrix 2 is 2. T F T F T F T F
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
True or False
![(e) A set of vectors \(\vec{0}, \vec{v}_1, \cdots, \vec{v}_k\) is always linearly independent.
\[ \text{T} \quad \text{F} \]
(f) A basis for \(\mathbb{R}^3\) can consist of 2 vectors.
\[ \text{T} \quad \text{F} \]
(g) \((A^T)^T = A\).
\[ \text{T} \quad \text{F} \]
(h) The rank of a \(2 \times 2\) matrix \(\begin{bmatrix} 1 & 1 \\ 2 & 2 \end{bmatrix}\) is 2.
\[ \text{T} \quad \text{F} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc52b3a7d-5814-4bdd-8c26-96eede61577b%2F4320d22b-20a0-4d2a-9ce4-8b2a2539f98a%2F571mc4_processed.png&w=3840&q=75)
Transcribed Image Text:(e) A set of vectors \(\vec{0}, \vec{v}_1, \cdots, \vec{v}_k\) is always linearly independent.
\[ \text{T} \quad \text{F} \]
(f) A basis for \(\mathbb{R}^3\) can consist of 2 vectors.
\[ \text{T} \quad \text{F} \]
(g) \((A^T)^T = A\).
\[ \text{T} \quad \text{F} \]
(h) The rank of a \(2 \times 2\) matrix \(\begin{bmatrix} 1 & 1 \\ 2 & 2 \end{bmatrix}\) is 2.
\[ \text{T} \quad \text{F} \]
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