Question Number 56141 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:\left(\mathrm{1}+{x}\right)^{{n}} ={C}_{\mathrm{0}} +{C}_{\mathrm{1}} {x}+{C}_{\mathrm{2}} {x}^{\mathrm{2}} +…+{C}_{{n}} {x}^{{n}} ,\:\mathrm{then} \\ $$$$\mathrm{for}\:{n}\:\mathrm{odd},\:{C}_{\mathrm{0}} \:^{\mathrm{2}} −{C}_{\mathrm{1}} \:^{\mathrm{2}} +{C}_{\mathrm{2}} \:^{\mathrm{2}} −{C}_{\mathrm{3}}…
Question Number 56140 by gunawan last updated on 11/Mar/19 $$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\:\: \\ $$$$\mathrm{2}\:{C}_{\mathrm{0}} +\frac{\mathrm{2}^{\mathrm{2}} }{\mathrm{2}}{C}_{\mathrm{1}} +\frac{\mathrm{2}^{\mathrm{3}} }{\mathrm{3}}{C}_{\mathrm{2}} +\frac{\mathrm{2}^{\mathrm{4}} }{\mathrm{4}}{C}_{\mathrm{3}} +…+\frac{\mathrm{2}^{\mathrm{11}} }{\mathrm{11}}{C}_{\mathrm{10}} \:\:\mathrm{is} \\ $$ Answered by…
Question Number 56138 by gunawan last updated on 11/Mar/19 $$\mathrm{The}\:\mathrm{pisitive}\:\mathrm{value}\:\mathrm{of}\:\:{a}\:\mathrm{so}\:\mathrm{that}\:\mathrm{the} \\ $$$$\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{and}\:{x}^{\mathrm{15}} \:\mathrm{are}\:\mathrm{equal}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{expansion}\:\mathrm{of}\:\left({x}^{\mathrm{2}} +\:\frac{{a}}{{x}^{\mathrm{3}} }\right)^{\mathrm{10}} \\ $$ Commented by maxmathsup by imad…
Question Number 56139 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:{x}+{y}=\mathrm{1},\:\mathrm{then}\:\:\underset{{r}=\mathrm{0}} {\overset{{n}} {\sum}}\:{r}^{\mathrm{2}} \:\:^{{n}} {C}_{{r}} \:{x}^{{r}} \:{y}^{{n}−{r}} \:\mathrm{equals} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on…
Question Number 56137 by gunawan last updated on 11/Mar/19 $$\mathrm{If}\:\left(\mathrm{1}+\mathrm{2}{x}+{x}^{\mathrm{2}} \right)^{{n}} \:=\:\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}\:{a}_{{r}} \:{x}^{{r}} ,\:\mathrm{then}\:{a}_{{r}} = \\ $$ Commented by maxmathsup by imad last…
Question Number 56095 by gunawan last updated on 10/Mar/19 $$\mathrm{The}\:\mathrm{coefficient}\:\mathrm{of}\:{x}^{\mathrm{5}} \:\mathrm{in}\:\mathrm{the}\:\mathrm{expansion}\:\mathrm{of} \\ $$$$\left(\mathrm{1}+{x}\right)^{\mathrm{21}} \:+\left(\mathrm{1}+{x}\right)^{\mathrm{22}} +…+\left(\mathrm{1}+{x}\right)^{\mathrm{30}} \:\:\mathrm{is} \\ $$ Answered by tanmay.chaudhury50@gmail.com last updated on 10/Mar/19…
Question Number 55846 by gunawan last updated on 05/Mar/19 $$\mathrm{If}\:{x},\:{y},\:{z}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{determinant} \\ $$$$\begin{vmatrix}{{a}+\mathrm{2}}&{{a}+\mathrm{3}}&{{a}+\mathrm{2}{x}}\\{{a}+\mathrm{3}}&{{a}+\mathrm{4}}&{{a}+\mathrm{2}{y}}\\{{a}+\mathrm{4}}&{{a}+\mathrm{5}}&{{a}+\mathrm{2}{z}}\end{vmatrix}\:\mathrm{is} \\ $$ Answered by math1967 last updated on 05/Mar/19 $$\begin{vmatrix}{\mathrm{a}+\mathrm{2}}&{\mathrm{a}+\mathrm{3}}&{\mathrm{a}+\mathrm{2x}}\\{\mathrm{a}+\mathrm{3}−\mathrm{a}−\mathrm{2}}&{\mathrm{a}+\mathrm{4}−\mathrm{a}−\mathrm{3}}&{\mathrm{a}+\mathrm{2y}−\mathrm{a}−\mathrm{2x}}\\{\mathrm{a}+\mathrm{4}−\mathrm{a}−\mathrm{3}}&{\mathrm{a}+\mathrm{5}−\mathrm{a}−\mathrm{4}}&{\mathrm{a}+\mathrm{2z}−\mathrm{a}−\mathrm{2y}}\end{vmatrix}\mathrm{R}_{\mathrm{2}} ^{'}…
Question Number 55844 by gunawan last updated on 05/Mar/19 $$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{an}\:\mathrm{involutory}\:\mathrm{matrix},\:\mathrm{then}\: \\ $$$$\left({I}+{A}\right)\left({I}−{A}\right)=\mathrm{0}. \\ $$ Answered by 121194 last updated on 05/Mar/19 $$\mathrm{a}\:\mathrm{involutory}\:\mathrm{matrix}\:\mathrm{is}\:\mathrm{a}\:\mathrm{matrix}\:\mathrm{that}\:\mathrm{is}\:\mathrm{it}\:\mathrm{own}\:\mathrm{inverse} \\ $$$${A}^{\mathrm{2}} ={I}…
Question Number 55845 by gunawan last updated on 05/Mar/19 $$\mathrm{If}\:{A}\:\mathrm{is}\:\mathrm{3}×\mathrm{4}\:\mathrm{matrix}\:\mathrm{and}\:{B}\:\mathrm{is}\:\mathrm{a}\:\mathrm{matrix}\:\mathrm{such} \\ $$$$\mathrm{that}\:{A}'{B}\:\mathrm{and}\:{BA}'\:\mathrm{are}\:\mathrm{both}\:\mathrm{defined}.\:\mathrm{Then} \\ $$$${B}\:\:\:\mathrm{is}\:\mathrm{of}\:\mathrm{the}\:\mathrm{type} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 55843 by gunawan last updated on 05/Mar/19 $$\mathrm{Consider}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations} \\ $$$${a}_{\mathrm{1}} {x}+{b}_{\mathrm{1}} {y}+{c}_{\mathrm{1}} {z}=\mathrm{0},\:{a}_{\mathrm{2}} {x}+{b}_{\mathrm{2}} {y}+{c}_{\mathrm{2}} {z}=\mathrm{0}\:, \\ $$$${a}_{\mathrm{3}} {x}+{b}_{\mathrm{3}} {y}+{c}_{\mathrm{3}} {z}=\mathrm{0}\:\:\mathrm{if} \\ $$$$\begin{vmatrix}{{a}_{\mathrm{1}}…