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}} ? \\ $$ Commented by…
Question Number 4638 by Yozzii last updated on 17/Feb/16 $${Let}\:\boldsymbol{\mathrm{P}}=\begin{pmatrix}{\mathrm{1}−{p}_{\mathrm{1}} }&{{p}_{\mathrm{2}} }\\{{p}_{\mathrm{1}} }&{\mathrm{1}−{p}_{\mathrm{2}} }\end{pmatrix}=\begin{pmatrix}{{a}_{\mathrm{1},\mathrm{1}} }&{{a}_{\mathrm{1},\mathrm{2}} }\\{{a}_{\mathrm{2},\mathrm{1}} }&{{a}_{\mathrm{2},\mathrm{2}} }\end{pmatrix} \\ $$$${and}\:{that}\:\boldsymbol{\mathrm{P}}^{{n}} \:{be}\:{the}\:{nth}\:{power}\:{of}\:\boldsymbol{\mathrm{P}}\:{evaluated} \\ $$$${as}\:\boldsymbol{\mathrm{P}}^{{n}} =\boldsymbol{\mathrm{P}}×\boldsymbol{\mathrm{P}}^{{n}−\mathrm{1}} ;{i}.{e}\:{by}\:{successive}\:…
Question Number 69954 by 20190927 last updated on 29/Sep/19 $$\mathrm{A}=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}\:\:\:\:\mathrm{find}\:\mathrm{A}^{\mathrm{n}} \\ $$ Commented by mathmax by abdo last updated on 29/Sep/19 $${A}\:=\begin{pmatrix}{\mathrm{1}\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{1}}\end{pmatrix}\:+\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}\:\:={I}\:+{J} \\ $$$${we}\:{have}\:{J}^{\mathrm{2}} =\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}\:.\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}\:=\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix}…
Question Number 135467 by benjo_mathlover last updated on 13/Mar/21 Answered by EDWIN88 last updated on 13/Mar/21 $$\begin{vmatrix}{\alpha\:\:\:\:\:\beta\:\:\:\:\:\:\gamma}\\{\beta\:\:\:\:\:\gamma\:\:\:\:\:\:\alpha}\\{\gamma\:\:\:\:\:\alpha\:\:\:\:\:\beta}\end{vmatrix}=\:\alpha\left(\beta\gamma−\alpha^{\mathrm{2}} \right)−\beta\left(\beta^{\mathrm{2}} −\alpha\gamma\right)+\gamma\left(\alpha\beta−\gamma^{\mathrm{2}} \right) \\ $$$$=\alpha\beta\gamma−\alpha^{\mathrm{3}} −\beta^{\mathrm{3}} +\alpha\beta\gamma+\alpha\beta\gamma−\gamma^{\mathrm{3}} \\…
Question Number 4389 by Yozzii last updated on 17/Jan/16 $$\int_{−\infty} ^{\infty} \int_{−\infty} ^{\infty} \sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }{exp}\left(\frac{−\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} +{y}^{\mathrm{2}} \right)\right){dydx}=? \\ $$ Commented by prakash jain last…