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- Question 1, Exercise 2.6
- {3}=0\cdots (i)\\ &x_{1}-2 x_{2}+3 x_{3}=0\cdots (ii)\\ &4 x_{1}+x_{2}-6 x_{3}=0\cdots (iii)\\ \end{al... m has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{array}{cccc} 2x_... d{array} \right] \end{align*} =====Question 1(ii)===== Solve the system of homogeneous linear equa... ad \text{(i)}\\ &x_1 + x_2 + x_3 = 0 \quad \text{(ii)}\\ &x_1 - 4x_2 + 3x_3 = 0 \quad \text{(iii)} \en
- Question 2, Exercise 2.6
- _{3}=0 \cdots(i)\\ &2 x_{1}+3 x_{2}-x_{3}=0\cdots(ii)\\ &3 x_{1}-2 x_{2}+4 x_{3}=0\cdots(iii)\\ \end{a... \ x_3 \end{array} \right]$ =====Question 2(ii)===== Find the value of $\lambda$ for which the s... i)}\\ &2 x_{1}+\lambda x_{2}+x_{3}=0 \quad \text{(ii)}\\ &x_{1}-2 x_{2}+\lambda x_{3}=0 \quad \text{(i... (i)} \\ 2x_{1} + 2x_{2} + x_{3} &= 0 \quad \text{(ii)} \\ x_{1} - 2x_{2} + 2x_{3} &= 0 \quad \text{(ii
- Question 3, Exercise 2.6
- 9}, \quad z = -\frac{63}{19}$$ =====Question 3(ii)===== Solve the system of linear equation by Gaus... uad \cdots (i) \\ 2x + 2y + 6z &= 1 \quad \cdots (ii) \\ 3x - 4y - 5z &= 3 \quad \cdots (iii) \end{ali... = 2 \quad \cdots (i) \\ 2y - z &= 3 \quad \cdots (ii) \\ x + 3y &= 5 \quad \cdots (iii) \end{align*} T
- Question 13, Exercise 2.2
- ix} 4 & 3 & 2 \\ 1 & -3 & 0 \end{pmatrix} \cdots (ii) \end{align*} From (i) we have \begin{align*} Y =... 7 \end{pmatrix} \end{align*} Put value of $Y$ in (ii), we have \begin{align*} X + 3\left(2X - \begin{
- Question 1, Exercise 2.1
- of A}&= 2\times 3\end{align} ===== Question 1(ii) ===== Find the order of the following matrix $B=
- Question 2, Exercise 2.1
- Solution. ** Rectangular matrix =====Question 1(ii)===== Identify the following matrix $B=\left[\beg
- Question 4, Exercise 2.1
- & 1 \\ 0 & 6 & 9 \end{bmatrix}$$ =====Question 4(ii)===== Find the transpose of the following matrix
- Question 1, Exercise 2.2
- & 4 \end{bmatrix} \end{align*} =====Question 1(ii)===== Construct a matrix $A=\left[a_{i j}\right]$
- Question 4, Exercise 2.2
- \end{array}\right]. \end{align*} =====Question 4(ii)===== Find $X$ if $$\begin{bmatrix}3 & 2 \\ 0 &
- Question 7, Exercise 2.2
- and the proof is complete. GOOD =====Question 7(ii)===== If $A=\left[\begin{array}{ll}3 & -4 \\ 1 &
- Question 1, Exercise 2.3
- \implies |A|&=15 \end{align*} =====Question 1(ii)===== Evaluate the determinant of the matrix $\le
- Question 2, Exercise 2.3
- 0 \end{array}\right]\) is: $-17$ =====Question 2(ii)===== Evaluate the determinant of the following
- Question 3, Exercise 2.3
- matrix $A$ is a singular matrix. =====Question 3(ii)===== Determine which of the matrix $\left[\begin
- Question 4, Exercise 2.3
- Thus, $\lambda = \dfrac{16}{23}$. =====Question 4(ii)===== Find the value of $\lambda$, so that the gi
- Question 5, Exercise 2.3
- frac{1}{3} \end{array}\right]$$ =====Question 5(ii)===== Find the multiplicative inverse of the foll