Question and Answers Forum

All Questions      Topic List

Matrices and Determinants Questions

Previous in All Question      Next in All Question      

Previous in Matrices and Determinants      Next in Matrices and Determinants      

Question Number 214447 by 2universe456 last updated on 08/Dec/24

Commented by Frix last updated on 08/Dec/24

=abc

$$={abc} \\ $$

Answered by Rasheed.Sindhi last updated on 09/Dec/24

determinant ((1,1,1,1),(1,(a+1),1,1),(1,1,(1+b),1),(1,1,1,(1+c))) Subtract C_1 from C_2 ,C_3 & C_4 = determinant ((1,0,0,0),(1,a,0,0),(1,0,b,0),(1,0,0,c)) = determinant ((a,0,0),(0,b,0),(0,0,c)) =a determinant ((b,0),(0,c)) =a(bc−0)=abc

$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{{a}+\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}+{b}}&{\mathrm{1}}\\{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}+{c}}\end{vmatrix}\: \\ $$$${Subtract}\:\mathrm{C}_{\mathrm{1}} \:{from}\:\mathrm{C}_{\mathrm{2}} ,\mathrm{C}_{\mathrm{3}} \:\&\:\mathrm{C}_{\mathrm{4}} \\ $$$$=\begin{vmatrix}{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{1}}&{{a}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{0}}&{{b}}&{\mathrm{0}}\\{\mathrm{1}}&{\mathrm{0}}&{\mathrm{0}}&{{c}}\end{vmatrix}\: \\ $$$$=\begin{vmatrix}{{a}}&{\mathrm{0}}&{\mathrm{0}}\\{\mathrm{0}}&{{b}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{0}}&{{c}}\end{vmatrix} \\ $$$$={a}\begin{vmatrix}{{b}}&{\mathrm{0}}\\{\mathrm{0}}&{{c}}\end{vmatrix}\: \\ $$$$={a}\left({bc}−\mathrm{0}\right)={abc} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com