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Question Number 139104 by I want to learn more last updated on 22/Apr/21 $$\mathrm{Make}\:\:\mathrm{r}\:\:\mathrm{subject}\:\mathrm{formula}:\:\:\:\:\:\mathrm{S}_{\mathrm{n}} \:\:=\:\:\:\frac{\mathrm{a}\left(\mathrm{1}\:\:\:−\:\:\:\mathrm{r}^{\mathrm{n}} \right)}{\mathrm{1}\:\:−\:\:\:\mathrm{r}} \\ $$ Commented by mr W last updated on…
Question Number 7196 by Tawakalitu. last updated on 15/Aug/16 Answered by Rasheed Soomro last updated on 18/Aug/16 $$\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}\\{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}\\{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}\\{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}\\{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}\\{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}\\{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}\\{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}\\{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}&{\mathrm{2}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}\end{bmatrix}\:\:\:\: \\ $$$${Subtracting}\:{each}\:{row}\left({start}\:{from}\:\mathrm{2}{nd}\:{row}\right)\:\:{from}\:{previous}\:{row} \\ $$$$\begin{bmatrix}{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{-\mathrm{9}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{4}}&{\mathrm{5}}&{\mathrm{6}}&{\mathrm{7}}&{\mathrm{8}}&{\mathrm{9}}&{\mathrm{10}}&{\mathrm{1}}\end{bmatrix}\:\:\:\:\:\:\:\: \\ $$$${Again}\:{subtracting}\:{each}\:{row}\:{from}\:{previous}\:{row} \\…
Question Number 6856 by Tawakalitu. last updated on 31/Jul/16 $${Prove}\:{that}\:{the}\:{set}\:{of}\:{all}\:{m}\:×\:{n}\:{matrices}\:{having}\:{entries}\:{in}\:{a} \\ $$$${field}\:{is}\:{a}\:{vector}\:{space}\:{over}\:{F}. \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com
Question Number 6251 by net last updated on 20/Jun/16 $$\mathrm{3}{x}−\mathrm{2}{y}−\mathrm{4}{z}=\mathrm{2} \\ $$$$\mathrm{3}{y}−\mathrm{4}{z}=−\mathrm{2} \\ $$$$\mathrm{2}{y}+\mathrm{6}{z}=−\mathrm{1} \\ $$ Answered by Rasheed Soomro last updated on 20/Jun/16 $$\mathrm{3}{x}−\mathrm{2}{y}−\mathrm{4}{z}=\mathrm{2}………\left({i}\right)…
Question Number 5963 by Ashis last updated on 07/Jun/16 $$\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{what}}\:\boldsymbol{\mathrm{value}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{k}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{system}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{has}}\:\boldsymbol{\mathrm{no}}\:\boldsymbol{\mathrm{solution}} \\ $$$$\boldsymbol{\mathrm{x}}+\mathrm{2}\boldsymbol{\mathrm{y}}+\mathrm{3}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$$$\mathrm{2}\boldsymbol{\mathrm{x}}+\boldsymbol{\mathrm{ky}}+\mathrm{5}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$$$\mathrm{3}\boldsymbol{\mathrm{x}}+\mathrm{4}\boldsymbol{\mathrm{y}}+\mathrm{7}\boldsymbol{\mathrm{z}}=\mathrm{1} \\ $$ Commented by Yozzii last updated on 07/Jun/16…
Question Number 5465 by 3 last updated on 15/May/16 $${i} \\ $$ Answered by FilupSmith last updated on 15/May/16 $${i}=\sqrt{−\mathrm{1}} \\ $$ Terms of Service…
Question Number 136457 by byaw last updated on 22/Mar/21 Commented by mr W last updated on 22/Mar/21 $${A},{B},{C}\:{are}\:{true}. \\ $$$${question}\:{D}\:{is}\:{not}\:{clear}.\:{one}\:{angle} \\ $$$${alone}\:{can}\:{not}\:{be}\:{complementary}. \\ $$$${if}\:{question}\:{D}\:{means}\:{that}\:{the}\:{angle} \\…
Question Number 4812 by sanusihammed last updated on 15/Mar/16 Commented by prakash jain last updated on 16/Mar/16 $$\mathrm{Isn}'\mathrm{t}\:\left({A}−{B}\right)^{{T}} ={A}^{{T}} −{B}^{{T}} ? \\ $$ Commented by…