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Category: Matrices and Determinants

JS-js-Given-a-matrix-A-3-2-5-4-and-A-2-A-2I-0-where-is-a-constant-I-1-0-0-1-If-B-3-2-5-1-then-A-1-B-

Question Number 108059 by john santu last updated on 14/Aug/20 $$\:\:\:\frac{\heartsuit{JS}\heartsuit}{°{js}°} \\ $$$${Given}\:{a}\:{matrix}\:{A}=\begin{pmatrix}{\:\:\:\mathrm{3}\:\:\:\:\:\:\:\mathrm{2}}\\{−\mathrm{5}\:\:\:−\mathrm{4}}\end{pmatrix} \\ $$$${and}\:{A}^{\mathrm{2}} +\flat{A}−\mathrm{2}{I}=\mathrm{0}\:{where}\:\flat\:{is}\:{a} \\ $$$${constant}\:,\:{I}=\begin{pmatrix}{\mathrm{1}\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\mathrm{1}}\end{pmatrix}.\:{If}\:{B}\:= \\ $$$$\begin{pmatrix}{−\mathrm{3}\flat\:\:\:\:\:\:\mathrm{2}}\\{\:\:\:\mathrm{5}\flat\:\:\:\:−\mathrm{1}}\end{pmatrix}\:,\:{then}\:{A}^{−\mathrm{1}} {B}\:=\: \\ $$ Answered by…

How-many-different-words-can-be-formed-with-the-same-letters-as-in-TINKUTARA-if-no-two-same-letters-are-next-to-each-other-

Question Number 107196 by mr W last updated on 09/Aug/20 $${How}\:{many}\:{different}\:{words}\:{can}\:{be} \\ $$$${formed}\:{with}\:{the}\:{same}\:{letters}\:{as}\:{in} \\ $$$${TINKUTARA}\:{if}\:{no}\:{two}\:{same}\:{letters} \\ $$$${are}\:{next}\:{to}\:{each}\:{other}. \\ $$ Commented by john santu last updated…

If-both-A-I-2-and-A-I-2-are-orthogonal-matrices-then-prove-that-A-2-3-4-I-

Question Number 41392 by rahul 19 last updated on 06/Aug/18 $$\mathrm{If}\:\mathrm{both}\:\mathrm{A}−\:\frac{\mathrm{I}}{\mathrm{2}}\:\mathrm{and}\:\mathrm{A}+\frac{\mathrm{I}}{\mathrm{2}}\:\mathrm{are}\:\mathrm{orthogonal} \\ $$$$\mathrm{matrices},\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\: \\ $$$$\mathrm{A}^{\mathrm{2}} =\:−\frac{\mathrm{3}}{\mathrm{4}}\:\mathrm{I}. \\ $$ Commented by rahul 19 last updated on…