Question Number 86021 by mathocean1 last updated on 26/Mar/20 $${E}\:{is}\:{a}\:{vectorial}\:{plan}\:{in}\:\mathbb{R}\:{with}\:{a}\:{base} \\ $$$${B}=\left(\overset{\rightarrow} {{i}},\overset{\rightarrow} {{j}}\right).\:{f}\:{is}\:{an}\:{endomorphism}\:{of}\:{E} \\ $$$${defined}\:\forall\:\overset{\rightarrow} {{u}}={x}\overset{\rightarrow} {{i}}+{y}\overset{\rightarrow} {{j}}\:{by}\:{f}\left(\overset{\rightarrow} {{u}}\right)=\left(−\mathrm{7}{x}−\mathrm{12}{y}\right)\overset{\rightarrow} {{i}}+\left(\mathrm{4}{x}+\mathrm{7}{y}\right)\overset{\rightarrow} {{j}}. \\ $$$$\left.\mathrm{1}\right)\:{Determinate}\:{f}\left(\overset{\rightarrow} {{i}}\right)\:{and}\:{f}\left(\overset{\rightarrow}…
Question Number 151028 by kalenis last updated on 17/Aug/21 Answered by amin96 last updated on 17/Aug/21 $$\begin{cases}{{x}+{y}−{z}=\mathrm{7}\:\:\:\:\:−}\\{{x}−{y}+\mathrm{2}{z}=\mathrm{3}}\\{\mathrm{2}{x}+{y}+{z}=\mathrm{9}}\end{cases}\Rightarrow\begin{cases}{\mathrm{2}{x}+{z}=\mathrm{10}}\\{\mathrm{10}+{y}=\mathrm{9}}\end{cases}\:\Rightarrow\begin{cases}{\mathrm{2}{x}+{z}=\mathrm{10}}\\{{y}=−\mathrm{1}}\end{cases} \\ $$$$\begin{cases}{{x}−{z}=\mathrm{8}}\\{{x}+\mathrm{2}{z}=\mathrm{2}}\end{cases}\:\:\begin{cases}{\mathrm{2}{x}−\mathrm{2}{z}=\mathrm{16}}\\{{x}+\mathrm{2}{z}=\mathrm{2}}\end{cases}\Rightarrow\mathrm{3}{x}=\mathrm{18}\:\:{x}=\mathrm{6} \\ $$$${x}−{z}=\mathrm{8}\:\:\Rightarrow\:\:{z}=−\mathrm{2}\:\:\:\:\:{answer}\:\:\left(\mathrm{6};\:\:−\mathrm{1};\:\:−\mathrm{2}\right) \\ $$ Terms of…
Question Number 19589 by gourav~ last updated on 13/Aug/17 $${Let}\:{A}\:{and}\:{B}\:{is}\:\mathrm{3}×\mathrm{3}\:{matrix}\:{of}\:{equal}\:{number} \\ $$$${where}\:{A}={symmetric}\:{matrix}\: \\ $$$$….{B}={skew}\:{symmetric}\:{matrix} \\ $$$${and}\:{the}\:{relation}…\:\left({A}+{B}\right)\left({A}−{B}\right)=\left({A}−{B}\right)\left({A}+{B}\right) \\ $$$${then}..{the}\:{value}\:{of}..\:…\:{k} \\ $$$$\:\:\:\:\left({AB}\right)^{{T}} =\left(−\mathrm{1}\right)^{{k}} \left({AB}\right) \\ $$$$\left({a}\right)\:−\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({c}\right)\:\mathrm{2} \\…
Question Number 19547 by dioph last updated on 12/Aug/17 $$\mathrm{A}\:\mathrm{matrix}\:\mathrm{has}\:{N}\:\mathrm{rows}\:\mathrm{and}\:\mathrm{2}{k}−\mathrm{1}\: \\ $$$$\mathrm{columns}.\:\mathrm{Each}\:\mathrm{column}\:\mathrm{is}\:\mathrm{filled}\:\mathrm{with} \\ $$$${M}\:\mathrm{ones}\:\mathrm{and}\:{N}−{M}\:\mathrm{zeros}. \\ $$$$\mathrm{A}\:\mathrm{given}\:\mathrm{row}\:{j}\:\mathrm{is}\:“{cool}''\:\mathrm{if}\:\mathrm{and}\:\mathrm{only}\:\mathrm{if} \\ $$$$\underset{{i}=\mathrm{1}} {\overset{\mathrm{2}{k}−\mathrm{1}} {\sum}}{a}_{{ji}} \:\geqslant\:{k}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{number}\:\mathrm{of}\:\mathrm{cool}\:\mathrm{rows} \\ $$$$\mathrm{for}\:\mathrm{given}\:{N},\:{k}\:\mathrm{and}\:{M}.…
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Question Number 84068 by Power last updated on 09/Mar/20 Commented by Power last updated on 09/Mar/20 $$\boldsymbol{\mathrm{prove}}\:\boldsymbol{\mathrm{it}}\:\boldsymbol{\mathrm{please}} \\ $$ Commented by Power last updated on…
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Question Number 84001 by Power last updated on 08/Mar/20 Commented by Power last updated on 08/Mar/20 $$\mathrm{prove}\:\mathrm{it}\:\mathrm{pls} \\ $$ Commented by Power last updated on…
Question Number 149116 by bramlexs22 last updated on 03/Aug/21 $$\:\mathrm{If}\:\mathrm{A}\:\mathrm{is}\:\mathrm{a}\:\mathrm{3}×\mathrm{3}\:\mathrm{matrix}\:\mathrm{where}\:\mathrm{det}\left(\mathrm{A}\right)=−\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{what}\:\mathrm{will}\:\mathrm{be}\:\mathrm{det}\left(\mathrm{3A}^{\mathrm{2}} \mathrm{A}^{−\mathrm{1}} \right)? \\ $$$$\mathrm{knowing}\:\mathrm{that}\:\mathrm{A}^{−\mathrm{1}} \:\mathrm{is}\:\mathrm{the}\:\mathrm{inverse} \\ $$$$\mathrm{of}\:\mathrm{A}\: \\ $$ Answered by EDWIN88 last…
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