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Category: Matrices and Determinants

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}= \\…

Given-matrix-A-a-1-1-1-a-1-1-1-a-If-B-b-A-and-B-is-orthogonal-determine-value-of-a-and-b-

Question Number 115520 by bemath last updated on 26/Sep/20 $${Given}\:{matrix}\:{A}\:=\:\begin{pmatrix}{{a}\:\:\:\mathrm{1}\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:{a}\:\:\:\:\mathrm{1}}\\{\mathrm{1}\:\:\:\:\mathrm{1}\:\:\:\:{a}}\end{pmatrix}\: \\ $$$${If}\:{B}\:=\:{b}.{A}\:{and}\:{B}\:{is}\:{orthogonal}\: \\ $$$${determine}\:{value}\:{of}\:{a}\:{and}\:{b}. \\ $$ Answered by bobhans last updated on 26/Sep/20 $${B}\:=\:\begin{pmatrix}{{ab}\:\:\:\:{b}\:\:\:\:\:{b}}\\{{b}\:\:\:\:\:\:{ab}\:\:\:\:{b}}\\{{b}\:\:\:\:\:\:{b}\:\:\:\:\:\:{ab}}\end{pmatrix}\:\:\Rightarrow\:\left({ab}\right)^{\mathrm{2}} +{b}^{\mathrm{2}}…

If-determinant-a-a-2-1-a-3-b-b-2-1-b-3-c-c-2-1-c-3-0-a-b-c-a-b-c-

Question Number 115508 by bemath last updated on 26/Sep/20 $${If}\begin{vmatrix}{{a}\:\:\:\:{a}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{1}+{a}^{\mathrm{3}} }\\{{b}\:\:\:\:{b}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{1}+{b}^{\mathrm{3}} }\\{{c}\:\:\:\:{c}^{\mathrm{2}} \:\:\:\:\:\:\:\mathrm{1}+{c}^{\mathrm{3}} }\end{vmatrix}=\:\mathrm{0} \\ $$$${a}\neq{b}\neq{c}\:\rightarrow\begin{cases}{{a}\:=?}\\{{b}=?\:}\\{{c}=?}\end{cases} \\ $$ Answered by bobhans last updated…