Question

Proving linear independence of transformed vectors from the linear independence of initial vectors.

score 25 · Answer 1 · 2020-02-24 13:46:43

25

Views

Proving linear independence of transformed vectors from the linear independence of initial vectors.

Published on 24 Feb 2020 - 13:46

score 246 · Answer 2 · 2020-02-24 15:51:16

246

Views

Proof verification: $\dim(U_1 \cap U_2) = \dim(f(U_1) \cap f(U_2))$

Published on 24 Feb 2020 - 15:51

score 67 · Answer 3 · 2026-03-26 04:34:54

67

Views

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

Published on 26 Mar 2026 - 4:34

score 91 · Answer 4 · 2026-03-29 14:02:10

91

Views

Prove that $\lim_{x\to 3} (2x^2-5)=13$

Published on 29 Mar 2026 - 14:02

score 72 · Answer 5 · 2026-03-28 21:06:46

72

Views

Solving $\lfloor \sqrt{9n^2+1}\rfloor+\lfloor\sqrt{9n^2+2}\rfloor+...+\lfloor\sqrt{9n^2+24n}\rfloor=349 $

Published on 28 Mar 2026 - 21:06

score 186 · Answer 6 · 2020-02-24 19:14:00

186

Views

Prove that $3^{4n-1}-2$ is always a multiple of 5.

Published on 24 Feb 2020 - 19:14

score 70 · Answer 7 · 2026-03-28 06:13:22

70

Views

If $\Phi: G \to G'$ is onto and $H \lhd G$, then $\Phi(H) \lhd G'$.

Published on 28 Mar 2026 - 6:13

score 651 · Answer 8 · 2026-04-02 09:27:30

651

Views

Find all the relative extrema of the function $f(x)=2x-24x^{1/3}$

Published on 02 Apr 2026 - 9:27

score 987 · Answer 9 · 2026-04-02 09:27:32

987

Views

Find the relative maximum and relative minimum of the function $f(x) = 49x + \frac{4}{x}$

Published on 02 Apr 2026 - 9:27

score 72 · Answer 10 · 2020-02-24 23:46:30

72

Views

Prove that $a_n \to a$ implies $\frac{\sum_{i=1}^n a_i}{n} \to a$

Published on 24 Feb 2020 - 23:46

score 29 · Answer 11 · 2020-02-25 01:41:17

29

Views

Proof for $f(n) \in O(n)$ implies $[f(n)]^2 \in O(n^2)$.

Published on 25 Feb 2020 - 1:41

score 2.2k · Answer 12 · 2026-03-29 14:06:48

2.2k

Views

Show that $(U + W)^{\perp} = U^{\perp}\cap W^{\perp}$ and $U^{\perp} + W^{\perp} \subset (U\cap W)^{\perp}$

Published on 29 Mar 2026 - 14:06

score 215 · Answer 13 · 2020-02-25 08:17:19

Proof-Check : Let $R$ be a finite commutative ring with unity. Prove that every nonzero element of $R$ is either a unit or a zero-divisor.

score 158 · Answer 14 · 2020-02-25 08:30:46

158

Views

If $A,B,C$ are events on a probability space then $P(A\cap B\cap C)\geq P(A)+P(B)+P(C)-2$

Published on 25 Feb 2020 - 8:30

score 21 · Answer 15 · 2020-02-25 09:21:32

21

Views

If $X$ is a random variable then the function $G(t)=P(\{X<t\})$ is left-continuous

Published on 25 Feb 2020 - 9:21

List Question

Proving linear independence of transformed vectors from the linear independence of initial vectors.

Proof verification: $\dim(U_1 \cap U_2) = \dim(f(U_1) \cap f(U_2))$

Show that, if girth$(G) \geq g, \text{and } \delta(G) \geq d$, then $|V(G)|= n = \Omega(d^k), \text{where } k = \lfloor \frac{g-1}{2} \rfloor$.

Prove that $\lim_{x\to 3} (2x^2-5)=13$

Solving $\lfloor \sqrt{9n^2+1}\rfloor+\lfloor\sqrt{9n^2+2}\rfloor+...+\lfloor\sqrt{9n^2+24n}\rfloor=349 $

Prove that $3^{4n-1}-2$ is always a multiple of 5.

If $\Phi: G \to G'$ is onto and $H \lhd G$, then $\Phi(H) \lhd G'$.

Find all the relative extrema of the function $f(x)=2x-24x^{1/3}$

Find the relative maximum and relative minimum of the function $f(x) = 49x + \frac{4}{x}$

Prove that $a_n \to a$ implies $\frac{\sum_{i=1}^n a_i}{n} \to a$

Proof for $f(n) \in O(n)$ implies $[f(n)]^2 \in O(n^2)$.

Show that $(U + W)^{\perp} = U^{\perp}\cap W^{\perp}$ and $U^{\perp} + W^{\perp} \subset (U\cap W)^{\perp}$

Proof-Check : Let $R$ be a finite commutative ring with unity. Prove that every nonzero element of $R$ is either a unit or a zero-divisor.

If $A,B,C$ are events on a probability space then $P(A\cap B\cap C)\geq P(A)+P(B)+P(C)-2$

If $X$ is a random variable then the function $G(t)=P(\{X<t\})$ is left-continuous

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