Question

Is $L$ an isomorphism?

score 89 · Answer 1 · 2026-04-12 11:54:18

89

Views

Is $L$ an isomorphism?

Published on 12 Apr 2026 - 11:54

score 72 · Answer 2 · 2026-04-15 20:02:36

72

Views

Finding all order-$2$ elements in the set of $2 \times 2$ matrices with determinant $1$

Published on 15 Apr 2026 - 20:02

score 65 · Answer 3 · 2026-04-09 13:38:14

65

Views

Let $N$ be a square matrix with $N^m \neq 0$ for $m \in \mathbb{N}$, while $N^{m+1} = 0$. Show that the matrices $I_n, N, N^2, ..., N^m$ are l.i.

Published on 09 Apr 2026 - 13:38

score 180 · Answer 4 · 2026-04-17 08:25:29

180

Views

The average of 10 scores is $25,$ and the lowest score is $20.$ So, the highest score must be...

Published on 17 Apr 2026 - 8:25

score 47 · Answer 5 · 2026-04-11 15:35:22

47

Views

Is the property already proven by the definition?

Published on 11 Apr 2026 - 15:35

score 32 · Answer 6 · 2026-04-16 08:30:17

32

Views

Apostol, Ch. 1 Linear Spaces: Replace positivity axiom with $(x,x)=0 \iff x=O$. Prove $(x,x)>0$ for all $x\neq O$ or else $(x,x)<0$ for all $x\neq O$.

Published on 16 Apr 2026 - 8:30

score 90 · Answer 7 · 2026-04-15 14:35:53

90

Views

Evaluate $\lim_{n\to\infty}\sum_{k=1}^n\frac{n}{n^2+k^2}$

Published on 15 Apr 2026 - 14:35

score 139 · Answer 8 · 2026-04-16 15:01:58

139

Views

$\displaystyle\lim_{n\to\infty} n\log \left(\frac{n+1}{n}\right )$

Published on 16 Apr 2026 - 15:01

score 71 · Answer 9 · 2026-04-17 14:30:20

71

Views

Does the integral $\int_{1}^{\infty} \frac{\operatorname{arctg}(\sqrt{1 + x^{2}})}{x+3}dx$ converge?

Published on 17 Apr 2026 - 14:30

score 152 · Answer 10 · 2026-04-09 06:04:37

152

Views

Find integer solutions to $x^2y + xy^2 = 240$

Published on 09 Apr 2026 - 6:04

score 29 · Answer 11 · 2026-04-16 00:23:49

29

Views

find a basis $W$ of $\mathbb{R}^4$ and a basis $B$ of $\mathbb{R}^3$ with change-of-basis matrix is $M_B^W(F)$.

Published on 16 Apr 2026 - 0:23

score 35 · Answer 12 · 2026-04-10 19:38:26

35

Views

How exactly does Tom Apostol's proof of the limit quotient property work?

Published on 10 Apr 2026 - 19:38

score 73 · Answer 13 · 2026-04-15 03:27:27

73

Views

Prove that there is only one $f$ using the Existence and Uniqueness Theorem for Ordinary Differential Equations

Published on 15 Apr 2026 - 3:27

score 59 · Answer 14 · 2026-04-16 02:48:47

59

Views

Prove the difference of 2 solutions of different initial values problems is increasing with time

Published on 16 Apr 2026 - 2:48

score 142 · Answer 15 · 2026-04-12 15:41:52

142

Views

The set of all sets does not exist

Published on 12 Apr 2026 - 15:41

List Question

Is $L$ an isomorphism?

Finding all order-$2$ elements in the set of $2 \times 2$ matrices with determinant $1$

Let $N$ be a square matrix with $N^m \neq 0$ for $m \in \mathbb{N}$, while $N^{m+1} = 0$. Show that the matrices $I_n, N, N^2, ..., N^m$ are l.i.

The average of 10 scores is $25,$ and the lowest score is $20.$ So, the highest score must be...

Is the property already proven by the definition?

Apostol, Ch. 1 Linear Spaces: Replace positivity axiom with $(x,x)=0 \iff x=O$. Prove $(x,x)>0$ for all $x\neq O$ or else $(x,x)<0$ for all $x\neq O$.

Evaluate $\lim_{n\to\infty}\sum_{k=1}^n\frac{n}{n^2+k^2}$

$\displaystyle\lim_{n\to\infty} n\log \left(\frac{n+1}{n}\right )$

Does the integral $\int_{1}^{\infty} \frac{\operatorname{arctg}(\sqrt{1 + x^{2}})}{x+3}dx$ converge?

Find integer solutions to $x^2y + xy^2 = 240$

find a basis $W$ of $\mathbb{R}^4$ and a basis $B$ of $\mathbb{R}^3$ with change-of-basis matrix is $M_B^W(F)$.

How exactly does Tom Apostol's proof of the limit quotient property work?

Prove that there is only one $f$ using the Existence and Uniqueness Theorem for Ordinary Differential Equations

Prove the difference of 2 solutions of different initial values problems is increasing with time

The set of all sets does not exist

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