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Category: Matrices and Determinants

consider-a-non-singular-2-2-square-matrix-T-If-trace-T-4-and-trace-T-2-5-what-is-determinant-of-the-matrix-T-

Question Number 117973 by bemath last updated on 14/Oct/20 $$\mathrm{consider}\:\mathrm{a}\:\mathrm{non}−\mathrm{singular}\:\mathrm{2}×\mathrm{2}\: \\ $$$$\mathrm{square}\:\mathrm{matrix}\:\mathrm{T}.\:\mathrm{If}\:\mathrm{trace}\:\left(\mathrm{T}\right)\:=\mathrm{4} \\ $$$$\mathrm{and}\:\mathrm{trace}\:\left(\mathrm{T}^{\mathrm{2}} \right)=\mathrm{5}\:\mathrm{what}\:\mathrm{is}\:\mathrm{determinant} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{matrix}\:\mathrm{T}\:? \\ $$ Answered by bobhans last updated on…

find-the-rank-of-the-matrix-A-and-B-by-following-row-operation-A-1-2-3-1-2-1-3-1-1-0-1-1-0-1-1-1-B-1-2-1-4-2-4-3-

Question Number 183425 by ali009 last updated on 25/Dec/22 $${find}\:{the}\:{rank}\:{of}\:{the}\:{matrix}\:{A}\:{and}\:{B}\:{by} \\ $$$$\:{following}\:{row}\:{operation}: \\ $$$${A}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{2}}&{−\mathrm{1}}&{−\mathrm{3}}&{−\mathrm{1}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{1}}&{\:\:\:\:\mathrm{1}}\\{\mathrm{0}}&{\mathrm{1}}&{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix} \\ $$$${B}=\begin{bmatrix}{\:\:\:\:\mathrm{1}}&{\:\:\:\:\mathrm{2}}&{−\mathrm{1}}&{\:\:\:\:\:\mathrm{4}}\\{\:\:\:\:\mathrm{2}}&{\:\:\:\:\mathrm{4}}&{\:\:\:\:\:\mathrm{3}}&{\:\:\:\:\:\mathrm{5}}\\{−\mathrm{1}}&{−\mathrm{2}}&{\:\:\:\:\:\mathrm{6}}&{−\mathrm{7}}\end{bmatrix} \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

find-the-value-of-cofficent-in-the-following-system-from-the-determinat-2x-1-x-2-x-3-0-1-x-1-x-2-2x-3-0-4x-1-x-2-4x-3-0-

Question Number 183240 by ali009 last updated on 23/Dec/22 $${find}\:{the}\:{value}\:{of}\:{cofficent}\:\mu\:{in}\:{the}\:{following} \\ $$$${system}\:{from}\:{the}\:{determinat}: \\ $$$$\mathrm{2}{x}_{\mathrm{1}} +\mu{x}_{\mathrm{2}} +{x}_{\mathrm{3}} =\mathrm{0} \\ $$$$\left(\mu−\mathrm{1}\right){x}_{\mathrm{1}} −{x}_{\mathrm{2}} +\mathrm{2}{x}_{\mathrm{3}} =\mathrm{0} \\ $$$$\mathrm{4}{x}_{\mathrm{1}} +{x}^{\mathrm{2}}…

determine-eigenvalues-and-digonalize-by-row-operation-4-9-6-12-9-1-4-6-2-11-8-16-1-3-0-1-

Question Number 183239 by ali009 last updated on 24/Dec/22 $${determine}\:{eigenvalues}\:{and}\:{digonalize} \\ $$$${by}\:{row}\:{operation} \\ $$$$\begin{bmatrix}{\mathrm{4}}&{−\mathrm{9}}&{\mathrm{6}}&{\mathrm{12}}\\{\mathrm{9}}&{−\mathrm{1}}&{\mathrm{4}}&{\mathrm{6}}\\{\mathrm{2}}&{−\mathrm{11}}&{\mathrm{8}}&{\mathrm{16}}\\{−\mathrm{1}}&{\:\:\:\:\mathrm{3}}&{\mathrm{0}}&{−\mathrm{1}}\end{bmatrix} \\ $$$$ \\ $$ Terms of Service Privacy Policy Contact: info@tinkutara.com

Find-an-orthogonal-matrix-A-whose-first-row-is-u-1-1-3-2-3-2-3-

Question Number 116746 by bemath last updated on 06/Oct/20 $$\mathrm{Find}\:\mathrm{an}\:\mathrm{orthogonal}\:\mathrm{matrix}\:\mathrm{A}\:\mathrm{whose} \\ $$$$\mathrm{first}\:\mathrm{row}\:\mathrm{is}\:\mathrm{u}_{\mathrm{1}} =\:\left(\frac{\mathrm{1}}{\mathrm{3}},\:\frac{\mathrm{2}}{\mathrm{3}},\:\frac{\mathrm{2}}{\mathrm{3}}\right). \\ $$ Answered by john santu last updated on 06/Oct/20 $${First}\:{step}\:{find}\:{a}\:{nonzero}\:{vector}\: \\…

Solving-by-Gaussian-elimination-using-the-following-system-of-linear-equation-x-3y-2z-6-2x-4y-3z-8-3x-6y-8z-5-

Question Number 116695 by bemath last updated on 06/Oct/20 $$\mathrm{Solving}\:\mathrm{by}\:\mathrm{Gaussian}\:\mathrm{elimination} \\ $$$$\mathrm{using}\:\mathrm{the}\:\mathrm{following}\:\mathrm{system}\:\mathrm{of} \\ $$$$\mathrm{linear}\:\mathrm{equation}\:\begin{cases}{\mathrm{x}−\mathrm{3y}−\mathrm{2z}=\mathrm{6}}\\{\mathrm{2x}−\mathrm{4y}−\mathrm{3z}=\mathrm{8}}\\{−\mathrm{3x}+\mathrm{6y}+\mathrm{8z}=−\mathrm{5}}\end{cases} \\ $$ Answered by bobhans last updated on 06/Oct/20 $$\:\mathrm{Solving}\:\mathrm{by}\:\mathrm{Gaussian}\:\mathrm{elimination}\:\mathrm{using} \\…

solve-for-x-determinant-1-x-x-2-x-3-1-2-2-2-2-3-1-3-3-2-3-3-1-4-4-2-4-3-0-

Question Number 116578 by bobhans last updated on 05/Oct/20 $$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}\: \\ $$$$\:\begin{vmatrix}{\mathrm{1}\:\:\:\mathrm{x}\:\:\:\:\mathrm{x}^{\mathrm{2}} \:\:\:\:\mathrm{x}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{2}\:\:\:\:\mathrm{2}^{\mathrm{2}} \:\:\:\:\mathrm{2}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{3}\:\:\:\:\mathrm{3}^{\mathrm{2}} \:\:\:\:\mathrm{3}^{\mathrm{3}} }\\{\mathrm{1}\:\:\:\mathrm{4}\:\:\:\:\mathrm{4}^{\mathrm{2}} \:\:\:\:\mathrm{4}^{\mathrm{3}} }\end{vmatrix}=\:\mathrm{0} \\ $$ Answered by bemath…

A-a-b-c-2-3-6-0-2-5-and-B-1-2-4-0-3-9-1-2-2-A-B-1-3-1-8-d-31-5-4-e-find-the-missing-value-

Question Number 182050 by ali009 last updated on 03/Dec/22 $${A}=\begin{bmatrix}{{a}}&{{b}}&{{c}}\\{−\mathrm{2}}&{\mathrm{3}}&{\mathrm{6}}\\{\mathrm{0}}&{−\mathrm{2}}&{\mathrm{5}}\end{bmatrix}{and}\:{B}=\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{\mathrm{4}}\\{\mathrm{0}}&{\mathrm{3}}&{\mathrm{9}}\\{−\mathrm{1}}&{\mathrm{2}}&{\mathrm{2}}\end{bmatrix} \\ $$$${A}×{B}=\begin{bmatrix}{−\mathrm{1}}&{\mathrm{3}}&{−\mathrm{1}}\\{−\mathrm{8}}&{{d}}&{\mathrm{31}}\\{−\mathrm{5}}&{\mathrm{4}}&{{e}}\end{bmatrix}{find}\:{the}\:{missing}\:{value} \\ $$ Answered by cortano1 last updated on 04/Dec/22 $$\:\begin{bmatrix}{\:\:\:\mathrm{a}\:\:\:\:\:\mathrm{b}\:\:\:\:\:\:\mathrm{c}}\\{−\mathrm{2}\:\:\:\:\mathrm{3}\:\:\:\:\:\:\mathrm{6}}\\{\:\:\:\mathrm{0}\:\:−\mathrm{2}\:\:\:\:\:\mathrm{5}}\end{bmatrix}\begin{bmatrix}{\:\:\:\mathrm{1}\:\:\:\:\:\mathrm{2}\:\:\:\:\:\:\mathrm{4}}\\{\:\:\:\mathrm{0}\:\:\:\:\:\mathrm{3}\:\:\:\:\:\:\mathrm{9}}\\{−\mathrm{1}\:\:\:\:\mathrm{2}\:\:\:\:\:\mathrm{2}}\end{bmatrix}= \\ $$$$\:\:\begin{bmatrix}{\mathrm{a}−\mathrm{c}\:\:\:\:\:\:\mathrm{2a}+\mathrm{3b}+\mathrm{2c}\:\:\:\:\:\:\:\mathrm{4a}+\mathrm{9b}+\mathrm{2c}}\\{−\mathrm{8}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{17}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{31}}\\{−\mathrm{5}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:−\mathrm{8}}\end{bmatrix}= \\…