Question

How would the condition for linearity for function with multiple variable be given?

score 1.1k · Answer 1 · 2026-05-10 16:57:48

How would the condition for linearity for function with multiple variable be given?

Published on 10 May 2026 - 16:57

score 74 · Answer 2 · 2026-04-16 09:04:11

$\mathbf{z} = \alpha \mathbf{x} + (1 - \alpha)\mathbf{y}$ is a solution of the system of equations $A\mathbf{x} = \mathbf{b}$ for any real $\alpha$?

score 77 · Answer 3 · 2026-04-14 19:49:55

77

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Dimension of the subspace $\{ p(B) : p \text{ is a polynomial with real coefficients}\}$ where $B$ is a matrix

Published on 14 Apr 2026 - 19:49

score 169 · Answer 4 · 2026-04-14 10:36:20

169

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A matrix with more than $m$ columns may have more than one set of $m$-dimensional vectors with $m$ mutually linearly independent columns?

Published on 14 Apr 2026 - 10:36

score 1k · Answer 5 · 2026-05-15 16:07:59

1k

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Sheldon Axler 3.109 : How to interpret " range T' = $(null\;T)^0$ "?

Published on 15 May 2026 - 16:07

score 76 · Answer 6 · 2026-04-14 02:13:18

76

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If $A$ is a normal matrix over $\mathbb{R}$ and all the eigenvalues of $A$ are real, is $A$ always symmetric?

Published on 14 Apr 2026 - 2:13

score 232 · Answer 7 · 2026-05-14 19:36:35

232

Views

Row echelon form and determinant

Published on 14 May 2026 - 19:36

score 38 · Answer 8 · 2026-04-14 19:57:40

38

Views

Rank of certain matrix determined by blocks

Published on 14 Apr 2026 - 19:57

score 4.7k · Answer 9 · 2026-04-14 15:51:38

4.7k

Views

Why is the matrix invertible if its null space is zero?

Published on 14 Apr 2026 - 15:51

score 387 · Answer 10 · 2026-04-14 18:08:37

387

Views

Finding transformation matrix given the image vector and pre-image vector

Published on 14 Apr 2026 - 18:08

score 80 · Answer 11 · 2026-04-13 05:46:34

80

Views

Solving a system of equations with a parameter.

Published on 13 Apr 2026 - 5:46

score 160 · Answer 12 · 2026-04-19 04:06:12

160

Views

If a vector space $V$ is spanned by $\{v_1,v_2\}$ then any three vectors in $V$ is linearly dependent

Published on 19 Apr 2026 - 4:06

score 65 · Answer 13 · 2026-04-25 08:21:27

65

Views

Is this matrix consistent?

Published on 25 Apr 2026 - 8:21

score 499 · Answer 14 · 2026-04-17 00:30:51

499

Views

Prove that $\dim(V_1\cap V_2\cap V_3)=1$ or $\dim (V_1+V_2+V_3)=3$

Published on 17 Apr 2026 - 0:30

score 1.9k · Answer 15 · 2026-04-25 06:56:24

1.9k

Views

Operator norm of symmetric matrix

Published on 25 Apr 2026 - 6:56

List Question

How would the condition for linearity for function with multiple variable be given?

$\mathbf{z} = \alpha \mathbf{x} + (1 - \alpha)\mathbf{y}$ is a solution of the system of equations $A\mathbf{x} = \mathbf{b}$ for any real $\alpha$?

Dimension of the subspace $\{ p(B) : p \text{ is a polynomial with real coefficients}\}$ where $B$ is a matrix

A matrix with more than $m$ columns may have more than one set of $m$-dimensional vectors with $m$ mutually linearly independent columns?

Sheldon Axler 3.109 : How to interpret " range T' = $(null\;T)^0$ "?

If $A$ is a normal matrix over $\mathbb{R}$ and all the eigenvalues of $A$ are real, is $A$ always symmetric?

Row echelon form and determinant

Rank of certain matrix determined by blocks

Why is the matrix invertible if its null space is zero?

Finding transformation matrix given the image vector and pre-image vector

Solving a system of equations with a parameter.

If a vector space $V$ is spanned by $\{v_1,v_2\}$ then any three vectors in $V$ is linearly dependent

Is this matrix consistent?

Prove that $\dim(V_1\cap V_2\cap V_3)=1$ or $\dim (V_1+V_2+V_3)=3$

Operator norm of symmetric matrix

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