# Category: Matrices and Determinants

## If-A-M-2-2-det-A-0-A-3-A-2-A-Find-the-values-of-det-2A-I-

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…

## Find-all-possible-value-a-a-b-d-b-a-b-c-c-b-c-d-d-a-c-d-when-a-b-c-d-vary-over-positive-reals-

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…

## Question-199164

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…