Question and Answers Forum

All Questions Topic List

Matrices and DeterminantsQuestion and Answers: Page 1

Question Number 222418 Answers: 1 Comments: 0

Prove that: lim_(n→+∞) [ ln^2 (n)−2∫^( n) _( 0) ((lnt)/( (√(1+t^2 )))) dt ]= (π^2 /6)+ln^2 (2)

$$\mathrm{Prove}\:\mathrm{that}:\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left[\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{n}\right)−\mathrm{2}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\:\mathrm{dt}\:\right]=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}+\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$

Question Number 220968 Answers: 0 Comments: 0

Question Number 220403 Answers: 1 Comments: 0

Question Number 220365 Answers: 3 Comments: 0

Question Number 220278 Answers: 0 Comments: 0

Question Number 219076 Answers: 0 Comments: 0

Question Number 218354 Answers: 0 Comments: 0

Question Number 218046 Answers: 0 Comments: 0

Question Number 218045 Answers: 0 Comments: 0

Question Number 217085 Answers: 0 Comments: 2

Question Number 216764 Answers: 1 Comments: 0

solve x? (√x) + 11 = 0

$${solve}\:{x}? \\ $$$$\sqrt{{x}}\:+\:\mathrm{11}\:=\:\mathrm{0} \\ $$

Question Number 216755 Answers: 1 Comments: 0

Question Number 216526 Answers: 1 Comments: 0

Question Number 216525 Answers: 2 Comments: 0

Question Number 214713 Answers: 2 Comments: 0

Find matrix B if given AB=BA= (((0 0)),((0 0)) ) where A= (((5 3)),((5 3)) ) and B ≠ (((0 0)),((0 0)) )

$$\:\:\mathrm{Find}\:\mathrm{matrix}\:\mathrm{B}\:\mathrm{if}\:\mathrm{given}\:\mathrm{AB}=\mathrm{BA}=\begin{pmatrix}{\mathrm{0}\:\:\mathrm{0}}\\{\mathrm{0}\:\:\mathrm{0}}\end{pmatrix} \\ $$$$\:\:\mathrm{where}\:\mathrm{A}=\:\begin{pmatrix}{\mathrm{5}\:\:\:\mathrm{3}}\\{\mathrm{5}\:\:\:\mathrm{3}}\end{pmatrix}\:\mathrm{and}\:\mathrm{B}\:\neq\:\begin{pmatrix}{\mathrm{0}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{0}}\end{pmatrix} \\ $$$$ \\ $$

Question Number 214495 Answers: 0 Comments: 1

Question Number 214447 Answers: 1 Comments: 1

Question Number 213435 Answers: 0 Comments: 0

A ∈ M_(2×2) ,and ,det (A)≠0 : A^3 = A^2 + A ⇒ det ( A −2I )=?

$$ \\ $$$$\:\:\:\:\:\:\:{A}\:\in\:\mathrm{M}_{\mathrm{2}×\mathrm{2}} \:\:,{and}\:,{det}\:\left({A}\right)\neq\mathrm{0}\::\:\:\:{A}^{\mathrm{3}} \:=\:{A}^{\mathrm{2}} \:+\:{A} \\ $$$$\:\:\:\:\:\:\:\:\Rightarrow\:\:{det}\:\left(\:{A}\:−\mathrm{2}{I}\:\right)=? \\ $$$$\:\:\:\:\:\: \\ $$

Question Number 212844 Answers: 2 Comments: 1

S^2 = (((14 −5)),((10 −1)) ) .

$$\:\: \\ $$$$ \mathrm{S}^{\mathrm{2}} \:=\:\begin{pmatrix}{\mathrm{14}\:\:\:\:\:\:−\mathrm{5}}\\{\mathrm{10}\:\:\:\:\:\:−\mathrm{1}}\end{pmatrix}\:.\: \\ $$

Question Number 211902 Answers: 1 Comments: 1

Question Number 208624 Answers: 1 Comments: 0

Question Number 208359 Answers: 1 Comments: 1

Question Number 207931 Answers: 2 Comments: 0

Question Number 205586 Answers: 1 Comments: 0

Givem that the matrix A = ((3,1,5),(2,3,5),(5,1,6) ). If Adj. A = (((13),(-1),(-10)),((13),(-7),(-5)),((-13),2,7) ) (i) find A^(−1) (ii) Use the result in (i) to find the values of x, y and z that will satisfy the equations: 3x + y + 5z = 8 2x +3y + 5z = 0 5x + y + 6z = 13

$${Givem}\:{that}\:{the}\:{matrix}\:{A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{1}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{1}}&{\mathrm{6}}\end{pmatrix}.\: \\ $$$${If}\:{Adj}.\:{A}\:=\:\begin{pmatrix}{\mathrm{13}}&{-\mathrm{1}}&{-\mathrm{10}}\\{\mathrm{13}}&{-\mathrm{7}}&{-\mathrm{5}}\\{-\mathrm{13}}&{\mathrm{2}}&{\mathrm{7}}\end{pmatrix} \\ $$$$\left({i}\right)\:{find}\:{A}^{−\mathrm{1}} \\ $$$$\left({ii}\right)\:{Use}\:{the}\:{result}\:{in}\:\left({i}\right)\:{to}\:{find}\:{the} \\ $$$${values}\:{of}\:{x},\:{y}\:{and}\:{z}\:{that}\:{will}\:{satisfy}\:{the} \\ $$$${equations}: \\ $$$$\mathrm{3}{x}\:+\:{y}\:+\:\mathrm{5}{z}\:=\:\mathrm{8} \\ $$$$\mathrm{2}{x}\:+\mathrm{3}{y}\:+\:\mathrm{5}{z}\:=\:\mathrm{0} \\ $$$$\mathrm{5}{x}\:+\:{y}\:+\:\mathrm{6}{z}\:=\:\mathrm{13} \\ $$

Question Number 205306 Answers: 1 Comments: 0

Question Number 203687 Answers: 0 Comments: 0

Pg 1 Pg 2 Pg 3 Pg 4 Pg 5 Pg 6 Pg 7 Pg 8 Pg 9 Pg 10

Terms of Service

Contact: info@tinkutara.com