Question Number 205306 by peter frank last updated on 15/Mar/24 Answered by A5T last updated on 15/Mar/24 $$\mathrm{2}\left(\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{xy}\right)=\mathrm{450}\Rightarrow\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{xy}=\mathrm{225} \\ $$$$\Rightarrow{y}=\frac{\mathrm{225}−\mathrm{3}{x}^{\mathrm{2}} }{\mathrm{4}{x}}\Rightarrow{v}=\mathrm{3}{x}^{\mathrm{2}} {y}=\frac{\mathrm{3}{x}\left(\mathrm{225}−\mathrm{3}{x}^{\mathrm{2}} \right)}{\mathrm{4}}…
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Question Number 202371 by mnjuly1970 last updated on 25/Dec/23 $$ \\ $$$$\:\:\:{If}\:\:\:\:{A}\:\in\:{M}_{\mathrm{2}×\mathrm{2}} \:,\:{det}\left({A}\:\right)\neq\:\mathrm{0} \\ $$$$\:\:\:\:,\:\:{A}^{\:\mathrm{3}} \:=\:{A}^{\mathrm{2}} \:+{A}\:\Rightarrow\:{Find}\:{the}\: \\ $$$$\:\:\:\:{values}\:{of}\:\:\:{det}\:\left(\mathrm{2}{A}\:−{I}\:\right) \\ $$$$ \\ $$ Answered by…
Question Number 199847 by cortano12 last updated on 10/Nov/23 $$\:\mathrm{Find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{value}\: \\ $$$$\:\frac{\mathrm{a}}{\mathrm{a}+\mathrm{b}+\mathrm{d}\:}\:+\frac{\mathrm{b}}{\mathrm{a}+\mathrm{b}+\mathrm{c}}\:+\:\frac{\mathrm{c}}{\mathrm{b}+\mathrm{c}+\mathrm{d}}+\frac{\mathrm{d}}{\mathrm{a}+\mathrm{c}+\mathrm{d}}\: \\ $$$$\:\mathrm{when}\:\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\:\mathrm{vary}\:\mathrm{over}\:\mathrm{positive} \\ $$$$\:\mathrm{reals}\: \\ $$ Commented by Frix last updated on 10/Nov/23…
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Question Number 199155 by cortano12 last updated on 28/Oct/23 $$\:\underbrace{ } \\ $$ Commented by mr W last updated on 31/Oct/23 $${see}\:{Q}\mathrm{199270} \\ $$ Terms…
Question Number 199001 by mnjuly1970 last updated on 26/Oct/23 $$ \\ $$$$\:\mathrm{I}{f}\:,\mathrm{A}\:\in\:\mathrm{M}_{{n}×{n}} \:\:\:,\:\:\mathrm{A}^{\:\mathrm{2}} \:=\:\mathrm{A}\:,\mathrm{1}\neq\:{k}\:\in\mathbb{R}. \\ $$$$\:\:\:\mathrm{F}{ind}\:\:\:\:\left(\:\:\:\mathrm{I}\:−\:{k}\mathrm{A}\:\right)^{\:−\mathrm{1}} \:=\:?\: \\ $$ Answered by MM42 last updated on…
Question Number 198743 by mnjuly1970 last updated on 23/Oct/23 Answered by witcher3 last updated on 24/Oct/23 $$\left(\mathrm{A}−\mathrm{I}\right)\left(\mathrm{A}−\mathrm{I}\right)^{−} =\mathrm{I} \\ $$$$=\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)−\mathrm{I}\left(\mathrm{A}−\mathrm{I}\right)^{−} = \\ $$$$\mathrm{A}\left(\mathrm{A}−\mathrm{I}\right)^{−} −\left(\mathrm{A}−\mathrm{I}\right)^{−} =\mathrm{I}…