Question

Prove that $\det(M) = 0$ iff $f_i$ are linearly dependent, where $M_{ij}= \int f_i f_j dx$ and $f_i$ are real and continuous

score 137 · Answer 1 · 2026-04-16 12:11:23

137

Views

Prove that $\det(M) = 0$ iff $f_i$ are linearly dependent, where $M_{ij}= \int f_i f_j dx$ and $f_i$ are real and continuous

Published on 16 Apr 2026 - 12:11

score 58 · Answer 2 · 2026-04-14 12:46:45

58

Views

Number of possible combinations in the game

Published on 14 Apr 2026 - 12:46

score 80 · Answer 3 · 2026-04-19 21:37:37

80

Views

Is it true that if you understand the content well enough, you won't need to know the solution (proofs)

Published on 19 Apr 2026 - 21:37

score 90 · Answer 4 · 2026-04-15 06:09:50

90

Views

Why is $\int_{\pi/2}^0 \cos x dx$ negative?

Published on 15 Apr 2026 - 6:09

score 245 · Answer 5 · 2026-04-12 05:46:47

245

Views

Collatz-like problem involving prime factors

Published on 12 Apr 2026 - 5:46

score 56 · Answer 6 · 2026-04-11 03:10:37

56

Views

Finding the distribution of an integer function of a uniform RV

Published on 11 Apr 2026 - 3:10

score 40 · Answer 7 · 2026-04-14 12:46:08

40

Views

Number of imperfections in a fine copper wire

Published on 14 Apr 2026 - 12:46

score 88 · Answer 8 · 2026-04-12 02:25:27

88

Views

Counting ordered triples whose product is at most $n$

Published on 12 Apr 2026 - 2:25

score 524 · Answer 9 · 2026-04-16 18:36:48

Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. Find the number of subsets $A$ of $S$ such that $x \in A$ and $2x \in S \implies 2x \in A$.

score 108 · Answer 10 · 2026-04-15 06:15:30

108

Views

asymptotics of finite difference equations

Published on 15 Apr 2026 - 6:15

score 117 · Answer 11 · 2026-04-17 11:52:18

117

Views

Describe the set of real numbers $x$ which satisfy $2\log_{2x+3}x<1$.

Published on 17 Apr 2026 - 11:52

score 146 · Answer 12 · 2026-03-26 09:42:40

146

Views

Definition of the evaluation map as a universal element of a representation

Published on 26 Mar 2026 - 9:42

score 473 · Answer 13 · 2026-04-14 04:48:07

473

Views

Finding the set of values of k for which a modulus equation has exactly 4 roots

Published on 14 Apr 2026 - 4:48

score 585 · Answer 14 · 2026-04-17 05:10:26

585

Views

Let $GL(2,\mathbb{R})$ denote the set of all non-singular $2×2$ matrices with real entries.Show that $SL(2,\mathbb{R})$ is a normal subgroup of

Published on 17 Apr 2026 - 5:10

score 29 · Answer 15 · 2026-04-09 14:29:49

29

Views

Finding angle ABC problem

Published on 09 Apr 2026 - 14:29

List Question

Prove that $\det(M) = 0$ iff $f_i$ are linearly dependent, where $M_{ij}= \int f_i f_j dx$ and $f_i$ are real and continuous

Number of possible combinations in the game

Is it true that if you understand the content well enough, you won't need to know the solution (proofs)

Why is $\int_{\pi/2}^0 \cos x dx$ negative?

Collatz-like problem involving prime factors

Finding the distribution of an integer function of a uniform RV

Number of imperfections in a fine copper wire

Counting ordered triples whose product is at most $n$

Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10\}$. Find the number of subsets $A$ of $S$ such that $x \in A$ and $2x \in S \implies 2x \in A$.

asymptotics of finite difference equations

Describe the set of real numbers $x$ which satisfy $2\log_{2x+3}x<1$.

Definition of the evaluation map as a universal element of a representation

Finding the set of values of k for which a modulus equation has exactly 4 roots

Let $GL(2,\mathbb{R})$ denote the set of all non-singular $2×2$ matrices with real entries.Show that $SL(2,\mathbb{R})$ is a normal subgroup of

Finding angle ABC problem

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