Question

Let $V$ be vector space over field $K$ and $v_1, ...v_n \in V$ be linearly independent Show $v_1, v_1+v_2, ...v_1+v_2+...v_n$ are linearly independent

score 106 · Answer 1 · 2026-04-16 11:21:20

106

Views

Let $V$ be vector space over field $K$ and $v_1, ...v_n \in V$ be linearly independent Show $v_1, v_1+v_2, ...v_1+v_2+...v_n$ are linearly independent

Published on 16 Apr 2026 - 11:21

score 94 · Answer 2 · 2026-04-16 03:49:07

94

Views

For what $\lambda \in \mathbb{R}$ is this a spanning set (Erzeugendensystem) of the vector space $\mathbb{R}^3$ ? {(1, 3, 4), (1, λ, 5), (1, 4, 3)}

Published on 16 Apr 2026 - 3:49

score 204 · Answer 3 · 2026-04-16 22:43:24

204

Views

Prove that in $\mathbb{R}^2$ it holds: {$(a,c), (b,d)$} is linearly independent $\iff ad - bc \neq 0$

Published on 16 Apr 2026 - 22:43

score 43 · Answer 4 · 2026-04-13 00:07:25

43

Views

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Published on 13 Apr 2026 - 0:07

score 89 · Answer 5 · 2026-03-26 16:26:34

89

Views

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Published on 26 Mar 2026 - 16:26

score 71 · Answer 6 · 2026-04-13 03:33:11

71

Views

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Published on 13 Apr 2026 - 3:33

score 18 · Answer 7 · 2026-04-17 06:56:05

18

Views

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Published on 17 Apr 2026 - 6:56

score 291 · Answer 8 · 2026-04-13 18:06:08

291

Views

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Published on 13 Apr 2026 - 18:06

score 81 · Answer 9 · 2026-04-11 06:00:46

81

Views

How to know if an expression is a solution to a linear system?

Published on 11 Apr 2026 - 6:00

score 36 · Answer 10 · 2026-04-13 23:23:52

36

Views

Using overdetermined linear system of equations and least squares approximation for parameter estimation

Published on 13 Apr 2026 - 23:23

score 79 · Answer 11 · 2026-04-14 17:14:03

79

Views

Solution to the system $a_1\sin\theta+b_1\cos\theta=x+c_1$, $a_2\sin\theta+b_2\cos\theta=x+c_2$ does not satisfy initial equations

Published on 14 Apr 2026 - 17:14

score 69 · Answer 12 · 2026-04-16 04:09:59

69

Views

how many equations required to solve $v = \exp(j \cdot 2\pi \cdot (a \cdot \cos(\phi) \cdot \sin(\theta) + b \cdot \sin(\phi)))$

Published on 16 Apr 2026 - 4:09

score 212 · Answer 13 · 2026-04-17 00:38:30

212

Views

Roots of $ 16 x^5 - 20 x^3 + 5x + 1 = 0 $

Published on 17 Apr 2026 - 0:38

score 59 · Answer 14 · 2026-04-12 13:44:25

59

Views

Solving a non-linear sum of powers system of equation for a sum of higher powers

Published on 12 Apr 2026 - 13:44

score 22 · Answer 15 · 2026-04-14 07:36:03

22

Views

Efficiently determine a matrix using equations made out of its elements

Published on 14 Apr 2026 - 7:36

List Question

Let $V$ be vector space over field $K$ and $v_1, ...v_n \in V$ be linearly independent Show $v_1, v_1+v_2, ...v_1+v_2+...v_n$ are linearly independent

For what $\lambda \in \mathbb{R}$ is this a spanning set (Erzeugendensystem) of the vector space $\mathbb{R}^3$ ? {(1, 3, 4), (1, λ, 5), (1, 4, 3)}

Prove that in $\mathbb{R}^2$ it holds: {$(a,c), (b,d)$} is linearly independent $\iff ad - bc \neq 0$

How to ocnvert SPDE to a system of two equations?

How many roots in a system of quartic equations

What's the name for this method of putting the roots of a polynomial in a system of equations?

Irregular system of equations

Algebraic vs geometric approach different results confusion

How to know if an expression is a solution to a linear system?

Using overdetermined linear system of equations and least squares approximation for parameter estimation

Solution to the system $a_1\sin\theta+b_1\cos\theta=x+c_1$, $a_2\sin\theta+b_2\cos\theta=x+c_2$ does not satisfy initial equations

how many equations required to solve $v = \exp(j \cdot 2\pi \cdot (a \cdot \cos(\phi) \cdot \sin(\theta) + b \cdot \sin(\phi)))$

Roots of $ 16 x^5 - 20 x^3 + 5x + 1 = 0 $

Solving a non-linear sum of powers system of equation for a sum of higher powers

Efficiently determine a matrix using equations made out of its elements

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