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- Question 3, Exercise 2.6
- ====Question 3(i)===== Solve the system of linear equation by Gauss elimination method.\\ $2 x+3 y+4 z=2$\\ ... -2 y+z=-3$\\ ** Solution. ** Given the system of equations: \begin{align*} \begin{aligned} 2x + 3y + 4z &= ... ===Question 3(ii)===== Solve the system of linear equation by Gauss elimination method.\\ $5 x-2 y+z=2$\\ $2... 4 y-5 z=3$\\ ** Solution. ** Given the system of equations: \begin{align*} 5x - 2y + z &= 2 \quad \cdots (i
- Question 6, Exercise 2.6
- ===Question 6(i)===== Solve the system of linear equation by matrix inversion method.FIXME\\ $5 x+3 y+z=6$\... 2 y+4 z=25$\\ ** Solution. ** For this system of equations; we have \begin{align*} A &= \begin{bmatrix} 5 &... lign*} Therefore, the solution to the system of equations is: $$x = \frac{1}{11}, \quad y =\frac{119}{11},... ===Question 6(ii)===== Solve the system of linear equation by matrix inversion method.\\ $x+2 y-3 z=5$\\ $2
- Question 1, Exercise 2.6
- 1(i)===== Solve the system of homogeneous linear equation for non-trivial solution if exists\\ $ 2 x_{1}-3 ... x_{3}=0\cdots (iii)\\ \end{align*} For system of equation, \begin{align*} A &= \left[ \begin{array}{ccc} 2... 1(ii)===== Solve the system of homogeneous linear equation for non-trivial solution if exists\\ $2 x_{1}-3 x... \quad \text{(iii)} \end{align*} For the system of equations, we have: \begin{align*} A &= \left[ \begin{arra
- Question 4, Exercise 2.6
- ====Question 4(i)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-x_{2}-x_{3}=2$... 2\end{align*} Thus, the solution to the system of equations is: $$\boxed{x_1 = \frac{13}{3}, \quad x_2 = \fr... ==Question 4(ii)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-3 x_{2}+7 x_{3... =Question 4(iii)===== Solve the system of linear equation by Gauss-Jordan method.\\ $x_{1}+x_{2}+x_{3}=3$\\
- Question 5, Exercise 2.6
- ====Question 5(i)===== Solve the system of linear equation by using Cramer's rule.\\ $x_{1}+x_{2}+2 x_{3}=8$... ===Question 5(ii)===== Solve the system of linear equation by using Cramer's rule.\\ $2 x_{1}+2 x_{2}+x_{3}=... {align*} The solution set for the given system of equations using Cramer's rule is: $$( -\frac{1}{7}, \frac{... ==Question 5(iii)===== Solve the system of linear equation by using Cramer's rule.\\ $-2 x_{2}+3 x_{3}=1$\\
- Question 7 and 8, Exercise 2.6
- ht]$; find $A^{-1}$ and hence solve the system of equations.\\ $3 x+4 y+7 z=14 ; 2 x-y+3 z=4 ; \quad x+2 y-3... {-11}{62} \end{bmatrix}$$ Now given the system of equations: \begin{align*} 3x + 4y + 7z &= 14 \\ 2x - y + 3... d R_2-8R_3\quad R_1-13R_3 \end{align*} From above equation we get, \begin{align*} x_1&=1\\ x_2&=1\\ x_3&=1 \end{align*} Now solutions of above equations are; $$ \begin{bmatrix} \dfrac{-3}{62} & \dfrac{
- Question 1, Review Exercise
- $3$</collapse> vii. System of homogeneous linear equations has non-trivial solution if: * (a) $|A|>0$ ... $</collapse> viii. For non-homogeneous system of equations; the system is inconsistent if: * (a) $\ope... s</collapse> ix. For a system of non-homogeneous equations with three variables system will have unique sol... }=3$</collapse> x. A system of non- homogeneous equation having infinite many solutions can be solved by u
- Question 2, Exercise 2.6
- ambda$ for which the system of homogeneous linear equation may have non-trivial solution. Also solve the sys... ambda$ for which the system of homogeneous linear equation may have non-trivial solution. Also solve the sys... - 7x_{3} &= 0 \quad \text{(3)} \end{align*} From equation (1), we have \begin{align*} x_{1} &= 4x_{2} - 3x_
- Question 9 and 10, Exercise 2.6
- n. =====Question 9===== Show that the system of equations $2 x-y+3 z=\alpha ; 3 x+y-5 z=\beta ;-5 x-5 y+21