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- Question 4, Exercise 1.3 @math-11-nbf:sol:unit01
- 4(i)===== Solve the simultaneous system of linear equation with complex coefficients: $(1-i) z+(1+i) \omega=... (ii)===== Solve the simultaneous system of linear equation with complex coefficients: $2 i z+(3-2 i) \omega=... ga = 3-i \quad \cdots(3) \end{align} Multiplying equation (2) by $2i$, we get: \begin{align} &2i(1-2i) z +... \end{align} Now, substituting $\omega$ back into equation $(1)$ to find $z$: \begin{align} &2iz + (3-2i)\le
- Question 1, Exercise 2.6 @math-11-nbf:sol:unit02
- 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... (iii)===== Solve the system of homogeneous linear equation for non-trivial solution if exists\\ $x_{1}+x_{2}
- Question 2, Exercise 1.3 @math-11-nbf:sol:unit01
- abad, Pakistan. ====Question 2(i)==== Solve the equation by completing square: $z^{2}-6 z+2=0$. **Solutio... m \sqrt{7}\}$. ====Question 2(ii)==== Solve the equation by completing square: $-\dfrac{1}{2} z^{2}-5 z+2=... \sqrt{29}\}$ ====Question 2(iii)==== Solve the equation by completing square: $4 z^{2}+5 z=14$. **Soluti... 9}}{8}\right\}$ ====Question 2(iv)==== Solve the equation by completing square: $z^{2}=5 z-3$. **Solution.
- Question 3, Exercise 1.3 @math-11-nbf:sol:unit01
- stan. ====Question 3(i)==== Solve the quadratic equation: $\dfrac{1}{3} z^{2}+2 z-16=0$. **Solution.** Gi... \}$. ====Question 3(ii)==== Solve the quadratic equation: $z^{2}-\frac{1}{2} z+17=0$. **Solution.** Give... \} $ ====Question 3(iii)==== Solve the quadratic equation: $z^{2}-6 z+25=0$. **Solution.** Given $$ z^{2}... 4i\}$ ====Question 3(iv)==== Solve the quadratic equation: $z^{2}-9 z+11=0$. **Solution.** Given $$z^{2}
- Question 3, Exercise 2.6 @math-11-nbf:sol:unit02
- ====Question 3(i)===== Solve the system of linear equation by Gauss elimination method.\\ $2 x+3 y+4 z=2$\\ ... ===Question 3(ii)===== Solve the system of linear equation by Gauss elimination method.\\ $5 x-2 y+z=2$\\ $2... ==Question 3(iii)===== Solve the system of linear equation by Gauss elimination method.\\ $2 x+z=2$\\ $2 y-z... ===Question 3(iv)===== Solve the system of linear equation by Gauss elimination method.\\ $x+2 y+5 z=4$\\ $3
- Question 4, Exercise 2.6 @math-11-nbf:sol:unit02
- ====Question 4(i)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-x_{2}-x_{3}=2$... ==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 4(iv)===== Solve the system of linear equation by Gauss-Jordan method.\\ $2 x_{1}-7 x_{2}+10 x_{
- Question 5, Exercise 2.6 @math-11-nbf:sol:unit02
- ====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}=... ==Question 5(iii)===== Solve the system of linear equation by using Cramer's rule.\\ $-2 x_{2}+3 x_{3}=1$\\ ... ===Question 5(iv)===== Solve the system of linear equation by using Cramer's rule.\\ $2 x_{1}+x_{2}+3 x_{3}=
- Question 6, Exercise 2.6 @math-11-nbf:sol:unit02
- ===Question 6(i)===== Solve the system of linear equation by matrix inversion method.FIXME\\ $5 x+3 y+z=6$\... ===Question 6(ii)===== Solve the system of linear equation by matrix inversion method.\\ $x+2 y-3 z=5$\\ $2 ... ==Question 6(iii)===== Solve the system of linear equation by matrix inversion method.\\ $-x+3 y-5 z=0$\\ $2... ===Question 6(iv)===== Solve the system of linear equation by matrix inversion method.\\ $\dfrac{2}{x}+\dfra
- Question 5 and 6, Exercise 4.2 @math-11-nbf:sol:unit04
- = -73 \quad \cdots (2) \end{align*} Now, subtract equation (1) from equation (2): \begin{align*} \begin{array}{ccc} a_1& + 27d &= -73\\ \mathop{}\limits_{-}a_1 &\ma... = 43 \quad \cdots (2) \end{align*} Now, subtract equation (1) from equation (2): \begin{align*} \begin{array}{ccc} a_1 & + 10d &= 43\\ \mathop{}\limits_{-}a_1 &\math
- Question 2, Exercise 2.6 @math-11-nbf:sol:unit02
- ambda$ 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 4.8 @math-11-nbf:sol:unit04
- 2) \end{align*} Now, put $k+1=0 \implies k=-1$ in equation (2): \begin{align*} 1 &= (-1+2)A + 0 \\ \implies ... . \end{align*} Next, put $k+2=0 \implies k=-2$ in equation (2): \begin{align*} 1 &= 0 + (-2+1)B \\ \implies ... . \end{align*} Using the values of $A$ and $B$ in equation (1), we get \begin{align*} \frac{1}{(k+1)(k+2)} &
- Question 13, 14 and 15, Exercise 4.8 @math-11-nbf:sol:unit04
- Now, put $2k+3 = 0 \implies k = -\frac{3}{2}$ in equation (2): \begin{align*} 1 &= (2 \times \left(-\frac{3... Next, put $2k+9 = 0 \implies k = -\frac{9}{2}$ in equation (2): \begin{align*} 1 &= 0 + (2 \times \left(-\fr... . \end{align*} Using the values of $A$ and $B$ in equation (1), we get \begin{align*} \frac{1}{(2k+3)(2k+9)}
- Question 3 and 4, Exercise 4.2 @math-11-nbf:sol:unit04
- = -1 \quad \cdots (2) \end{align*} Now, subtract equation (1) from equation (2): \begin{align*} \begin{array}{ccc} a_1 & + 8d &= -1\\ \mathop{}\limits_{-}a_1 &\matho
- Unit 01: Complex Numbers (Solutions)
- e $z^2+a^2$ or $z^3-3z^2+z=5$ * Solve quadratic equation of the form $pz^2+qz+r=0$, by completing squares,
- Question 7, Exercise 1.4 @math-11-nbf:sol:unit01
- . =====Question 7(i)===== Convert the following equation in Cartesian form: $\arg (z-1)=-\dfrac{\pi}{4}$