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Category: Matrices and Determinants

1-5-3-4-6-7-9-2-8-9-5-7-6-4-3-1-8-2-

Question Number 100873 by EquationMaker2305 last updated on 29/Jun/20 $$\begin{bmatrix}{\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\\{\mathrm{4}}&{\mathrm{6}}&{\mathrm{7}}\\{\mathrm{9}}&{\mathrm{2}}&{\mathrm{8}}\end{bmatrix}+\begin{bmatrix}{\mathrm{9}}&{\mathrm{5}}&{\mathrm{7}}\\{\mathrm{6}}&{\mathrm{4}}&{\mathrm{3}}\\{\mathrm{1}}&{\mathrm{8}}&{\mathrm{2}}\end{bmatrix} \\ $$ Commented by Tinku Tara last updated on 29/Jun/20 $$\mathrm{Please}\:\mathrm{avoid}\:\mathrm{posting}\:\mathrm{question}\:\mathrm{for} \\ $$$$\mathrm{unless}\:\mathrm{you}\:\mathrm{are}\:\mathrm{really}\:\mathrm{looking}\:\mathrm{for} \\ $$$$\mathrm{inputs}\:\mathrm{or}\:\mathrm{some}\:\mathrm{discussion}.…

Question-35319

Question Number 35319 by Tinkutara last updated on 17/May/18 Answered by MJS last updated on 17/May/18 $$\mathrm{it}'\mathrm{s}\:\mathrm{just}\:\mathrm{multiplicating}\:\mathrm{and}\:\mathrm{factorising} \\ $$$$\mathrm{det}\begin{vmatrix}{{a}}&{{b}}&{{c}}\\{{d}}&{{e}}&{{f}}\\{{g}}&{{h}}&{{i}}\end{vmatrix}={aei}+{bfg}+{cdh}−{afh}−{bdi}−{ceg} \\ $$ Commented by Tinkutara last…

Given-A-1-2-1-2-a-b-If-A-3-A-2-then-2a-3b-

Question Number 166377 by cortano1 last updated on 19/Feb/22 $$\:\:\mathrm{Given}\:\mathrm{A}=\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\:\:\mathrm{a}\:\:\:\:\:\:\:\:\mathrm{b}}\end{pmatrix}\:.\:\mathrm{If}\:\mathrm{A}^{\mathrm{3}} =\:\mathrm{A}^{\mathrm{2}} \\ $$$$\:\mathrm{then}\:\mathrm{2a}−\mathrm{3b}=? \\ $$ Answered by bobhans last updated on 19/Feb/22 $$\:\:\mathrm{A}^{\mathrm{2}} =\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\:\:\mathrm{a}\:\:\:\:\:\:\:\mathrm{b}}\end{pmatrix}\:\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}}\\{\:\:\mathrm{a}\:\:\:\:\:\:\mathrm{b}}\end{pmatrix}\:=\:\begin{pmatrix}{\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}\:\:\:\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{2}}\mathrm{b}}\\{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}+\mathrm{ab}\:\:\:\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{a}+\mathrm{b}^{\mathrm{2}} }\end{pmatrix}…

A-matrix-2×2-amp-B-2-3-2-4-such-that-A-T-B-3A-T-5-4-1-1-so-find-det-4A-1-

Question Number 100664 by bobhans last updated on 28/Jun/20 $$\mathrm{A}\:\mathrm{matrix}\:\mathrm{2×2}\:\&\:\mathrm{B}\:=\:\begin{pmatrix}{−\mathrm{2}\:\:\:\:\mathrm{3}}\\{\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{4}}\end{pmatrix}\:\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{A}^{\mathrm{T}} \mathrm{B}+\mathrm{3A}^{\mathrm{T}} \:=\:\begin{pmatrix}{\:\:\:\mathrm{5}\:\:\:\:\mathrm{4}}\\{−\mathrm{1}\:\:\:\mathrm{1}}\end{pmatrix}\:\:\mathrm{so}\:\mathrm{find}\:\mathrm{det}\left(\mathrm{4A}^{−\mathrm{1}} \right) \\ $$ Answered by bramlex last updated on 28/Jun/20 $${A}^{{T}}…

find-all-2×2-matrices-A-such-that-A-3-3A-2-2-2-2-2-

Question Number 100650 by bobhans last updated on 28/Jun/20 $$\mathrm{find}\:\mathrm{all}\:\mathrm{2×2}\:\mathrm{matrices}\:\mathrm{A}\:\mathrm{such} \\ $$$$\mathrm{that}\:\mathrm{A}^{\mathrm{3}} −\mathrm{3A}^{\mathrm{2}} \:=\:\begin{pmatrix}{−\mathrm{2}\:\:\:\:\:−\mathrm{2}}\\{−\mathrm{2}\:\:\:\:\:\:−\mathrm{2}}\end{pmatrix} \\ $$ Answered by bramlex last updated on 28/Jun/20 $${let}\:{A}\:=\:\begin{pmatrix}{{a}\:\:\:\:\:{b}}\\{{c}\:\:\:\:\:{d}}\end{pmatrix} \\…

Given-matrix-A-3-1-4-1-2-5-0-2-6-find-adj-adj-A-

Question Number 100296 by bobhans last updated on 26/Jun/20 $$\mathcal{G}\mathrm{iven}\:\mathrm{matrix}\:\mathrm{A}\:=\:\begin{bmatrix}{\mathrm{3}\:\:\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{4}}\\{\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{5}}\\{\mathrm{0}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{6}}\end{bmatrix} \\ $$$$\mathrm{find}:\:\:\mathrm{adj}\left(\mathrm{adj}\:\mathrm{A}\right)\:? \\ $$ Answered by bemath last updated on 26/Jun/20 $$\mathrm{adj}\left(\mathrm{adj}\:\mathrm{A}\right)\:=\:\mid\mathrm{A}\mid^{\mathrm{n}−\mathrm{1}} \:.\mathrm{A} \\ $$$$\mathrm{A}_{\mathrm{3}×\mathrm{3}}…

hello-all-i-have-some-questions-1-what-is-the-riemann-hypothesis-2-how-did-they-determine-the-distance-to-the-sun-3-how-did-we-measure-the-speed-of-light-

Question Number 100068 by  M±th+et+s last updated on 24/Jun/20 $${hello}\:{all}\:{i}\:{have}\:{some}\:{questions}? \\ $$$$ \\ $$$$\left.\mathrm{1}\right){what}\:{is}\:{the}\:{riemann}\:{hypothesis}? \\ $$$$ \\ $$$$\left.\mathrm{2}\right){how}\:{did}\:{they}\:{determine}\:{the}\:{distance} \\ $$$${to}\:{the}\:{sun}? \\ $$$$ \\ $$$$\left.\mathrm{3}\right){how}\:{did}\:{we}\:{measure}\:{the}\:{speed}\:{of}\:{light}? \\…

Explain-Einstein-s-theory-of-Gravitation-and-explain-why-photons-don-t-fit-Newton-s-model-but-Einstein-s-

Question Number 99986 by Rio Michael last updated on 24/Jun/20 $$\mathrm{Explain}\:\mathrm{Einstein}'\mathrm{s}\:\mathrm{theory}\:\mathrm{of}\:\mathrm{Gravitation}\: \\ $$$$\mathrm{and}\:\mathrm{explain}\:\mathrm{why}\:\mathrm{photons}\:\mathrm{don}'\mathrm{t}\:\mathrm{fit}\:\mathrm{Newton}'\mathrm{s} \\ $$$$\mathrm{model}\:\mathrm{but}\:\mathrm{Einstein}'\mathrm{s}. \\ $$ Answered by mathmax by abdo last updated on…