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Category: Matrices and Determinants

Question-10268

Question Number 10268 by j.masanja06@gmail.com last updated on 01/Feb/17 Answered by sandy_suhendra last updated on 01/Feb/17 $$\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}+\mathrm{5}\right)\left(\mathrm{x}−\mathrm{1}\right)+\mathrm{6}+\mathrm{42}−\mathrm{6}\left(\mathrm{x}+\mathrm{5}\right)+\mathrm{6}\left(\mathrm{x}−\mathrm{3}\right)+\mathrm{7}\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{0} \\ $$$$\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} −\mathrm{10x}+\mathrm{8}=\mathrm{0} \\ $$$$\left(\mathrm{x}−\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} +\mathrm{2x}−\mathrm{8}\right)=\mathrm{0} \\…

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Question Number 10245 by j.masanja06@gmail.com last updated on 31/Jan/17 $$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{x}}&{\mathrm{y}}&{\mathrm{z}}\\{\mathrm{x}^{\mathrm{2}} }&{\mathrm{y}^{\mathrm{2}} }&{\mathrm{z}^{\mathrm{2}} }\end{vmatrix}=\left(\mathrm{x}−\mathrm{y}\right)\left(\mathrm{y}−\mathrm{z}\right)\left(\mathrm{z}−\mathrm{y}\right) \\ $$ Answered by prakash jain last updated on 31/Jan/17…

solve-the-eqution-determinant-x-3-1-1-7-x-5-1-6-6-x-1-0-

Question Number 10243 by j.masanja06@gmail.com last updated on 31/Jan/17 $$\mathrm{solve}\:\mathrm{the}\:\mathrm{eqution} \\ $$$$\:\:\:\:\:\begin{vmatrix}{\mathrm{x}−\mathrm{3}}&{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{7}}&{\mathrm{x}+\mathrm{5}}&{−\mathrm{1}}\\{−\mathrm{6}}&{\mathrm{6}}&{\mathrm{x}−\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

A-2-1-1-3-1-2-2-1-2-find-the-inverse-of-this-matrix-

Question Number 141193 by Eric002 last updated on 16/May/21 $${A}=\begin{bmatrix}{\mathrm{2}\:\:}&{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{3}}&{−\mathrm{1}}&{\mathrm{2}}\\{−\mathrm{2}}&{\mathrm{1}}&{\mathrm{2}}\end{bmatrix}{find}\:{the}\:{inverse}\:{of}\:\:{this}\:{matrix} \\ $$$$ \\ $$ Answered by bramlexs22 last updated on 16/May/21 $$\:{Cayley}−{Hamilton}\:{theorem} \\ $$$$\:\mid{A}−\lambda{I}\mid\:=\:\mathrm{0} \\…

Given-the-matrix-A-1-1-1-0-2-1-2-3-0-and-B-3-3-1-2-2-1-4-5-2-find-the-matrix-product-AB-and-BA-state-the-relationship-between-A-and-B-find-also-the-matri

Question Number 75099 by Rio Michael last updated on 07/Dec/19 $${Given}\:{the}\:{matrix}\: \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{1}}&{−\mathrm{1}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{2}}&{\:−\mathrm{1}}\\{\mathrm{2}}&{\mathrm{3}}&{\mathrm{0}}\end{pmatrix}\:\:{and}\:{B}=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{2}}&{−\mathrm{2}}&{\mathrm{1}}\\{−\mathrm{4}}&{−\mathrm{5}}&{\mathrm{2}}\end{pmatrix} \\ $$$${find}\:{the}\:{matrix}\:{product}\:{AB}\:{and}\:{BA} \\ $$$${state}\:{the}\:{relationship}\:{between}\:{A}\:{and}\:{B} \\ $$$${find}\:{also}\:{the}\:{matrix}\:{product}\:{BM},\:{where}\:{M}=\begin{pmatrix}{\mathrm{8}}\\{−\mathrm{7}}\\{\mathrm{1}}\end{pmatrix} \\ $$$${Hence}\:{solve}\:{the}\:{system}\:{of}\:{equations}: \\ $$$$\:\:{x}−{y}\:+\:{z}\:=\:\mathrm{8}, \\ $$$$\:\:\:\:\:\:\:\mathrm{2}{y}\:−{z}\:=−\mathrm{7},…

If-f-x-determinant-sec-2-x-1-1-cos-2-x-cos-2-x-csc-2-x-1-cos-2-x-tan-2-x-evaluate-0-pi-4-f-x-dx-

Question Number 140548 by liberty last updated on 09/May/21 $$\mathrm{If}\:\mathrm{f}\left(\mathrm{x}\right)=\begin{vmatrix}{\mathrm{sec}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\mathrm{csc}^{\mathrm{2}} \mathrm{x}}\\{\:\:\:\mathrm{1}\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} \mathrm{x}\:\:\:\:\:\:\mathrm{tan}\:\:^{\mathrm{2}} \mathrm{x}}\end{vmatrix} \\ $$$$\mathrm{evaluate}\:\underset{\mathrm{0}} {\overset{\pi/\mathrm{4}} {\int}}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{dx}. \\ $$ Answered by EDWIN88…

find-the-determinant-of-the-matrix-below-1-4-3-1-2-0-6-3-4-1-2-5-1-0-2-4-

Question Number 9285 by suci last updated on 28/Nov/16 $${find}\:{the}\:{determinant}\:{of}\:{the}\:{matrix}\:{below} \\ $$$$\begin{bmatrix}{\mathrm{1}}&{\mathrm{4}}&{−\mathrm{3}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{0}}&{\mathrm{6}}&{\mathrm{3}}\\{\mathrm{4}}&{−\mathrm{1}}&{\mathrm{2}}&{\mathrm{5}}\\{\mathrm{1}}&{\mathrm{0}}&{−\mathrm{2}}&{\mathrm{4}}\end{bmatrix} \\ $$ Answered by mrW last updated on 28/Nov/16 $$\mid\mathrm{A}\mid=\begin{vmatrix}{\mathrm{1}}&{\mathrm{4}}&{−\mathrm{3}}&{\mathrm{1}}\\{\mathrm{2}}&{\mathrm{0}}&{\mathrm{6}}&{\mathrm{3}}\\{\mathrm{4}}&{−\mathrm{1}}&{\mathrm{2}}&{\mathrm{5}}\\{\mathrm{1}}&{\mathrm{0}}&{−\mathrm{2}}&{\mathrm{4}}\end{vmatrix} \\ $$$$\mathrm{R4}−\mathrm{R1}\:\mathrm{and}\:\mathrm{R3}−\mathrm{R2}×\mathrm{2}: \\…

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Question Number 9286 by suci last updated on 28/Nov/16 $${find}\:{the}\:{determinant}\:{of}\:{the}\:{matrix}\:{below} \\ $$$$\begin{vmatrix}{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{5}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$ Answered by mrW last updated on 28/Nov/16 $$=\mathrm{5}×\begin{vmatrix}{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{4}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\ $$$$=\mathrm{5}×\left(−\mathrm{4}\right)×\begin{vmatrix}{\mathrm{0}}&{\mathrm{0}}&{\mathrm{1}}\\{\mathrm{0}}&{\mathrm{2}}&{\mathrm{0}}\\{\mathrm{3}}&{\mathrm{0}}&{\mathrm{0}}\end{vmatrix} \\…