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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{align*} For system of equation, \begin{align*} A &= \... m has non-trivial solution. \text{By}\quad(i)-2(ii), we have \begin{align*} &\begin{array}{cccc} 2x_... 2=2x_3\\ \end{align*} Put the value of $x_3$ in (iii), we have \begin{align*} &4 x_{1}+2x_{3}-6 x_{3}
- 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{align*} Homogenous system has non-trivial solution, i... \ 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
- Question 3, Exercise 2.6
- 9}, \quad z = -\frac{63}{19}$$ =====Question 3(ii)===== Solve the system of linear equation by Gaus... uad \cdots (i) \\ 2x + 2y + 6z &= 1 \quad \cdots (ii) \\ 3x - 4y - 5z &= 3 \quad \cdots (iii) \end{align*} The associated augmented matrix is: \begin{alig... of equations has no solution. =====Question 3(iii)===== Solve the system of linear equation by Gau
- Question 1, Exercise 2.1
- of A}&= 2\times 3\end{align} ===== Question 1(ii) ===== Find the order of the following matrix $B=... der of B}&= 3\times 2\end{align} ===== Question 1(iii)===== Find the order of the following matrix $C=
- Question 2, Exercise 2.1
- Solution. ** Rectangular matrix =====Question 1(ii)===== Identify the following matrix $B=\left[\beg... ** Solution. ** Square matrix =====Question 1(iii)===== Identify the following matrix $C=\left[\b
- Question 4, Exercise 2.1
- & 1 \\ 0 & 6 & 9 \end{bmatrix}$$ =====Question 4(ii)===== Find the transpose of the following matrix ... \\ 2 \\ 0 \end{array}\right] $$ =====Question 4(iii)===== Find the transpose of the following matrix
- Question 1, Exercise 2.2
- & 4 \end{bmatrix} \end{align*} =====Question 1(ii)===== Construct a matrix $A=\left[a_{i j}\right]$... 1 & 2 \end{bmatrix} \end{align*} =====Question 1(iii)===== Construct a matrix $A=\left[a_{i j}\right]
- Question 4, Exercise 2.2
- \end{array}\right]. \end{align*} =====Question 4(ii)===== Find $X$ if $$\begin{bmatrix}3 & 2 \\ 0 & ... nd{bmatrix}.$$ ** Solution. ** =====Question 4(iii)===== If $A=\left[\begin{array}{ll}3 & 7\end{arr
- 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 2.3
- \implies |A|&=15 \end{align*} =====Question 1(ii)===== Evaluate the determinant of the matrix $\le... \implies |A| &= 1 \end{align*} =====Question 1(iii)===== Evaluate the determinant of the matrix $\l
- Question 2, Exercise 2.3
- 0 \end{array}\right]\) is: $-17$ =====Question 2(ii)===== Evaluate the determinant of the following ... & 4 \end{array}\right]\) is:$27$ =====Question 2(iii)===== 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... ix $A$ is a non-singular matrix. =====Question 3(iii)===== Determine which of the matrix $\left[\begi
- Question 4, Exercise 2.3
- Thus, $\lambda = \dfrac{16}{23}$. =====Question 4(ii)===== Find the value of $\lambda$, so that the gi... \\ \lambda = 4 \end{align*} =====Question 4(iii)===== Find the value of $\lambda$, so that the g
- Question 5, Exercise 2.3
- frac{1}{3} \end{array}\right]$$ =====Question 5(ii)===== Find the multiplicative inverse of the foll... ** Solution. ** Do yourself. =====Question 5(iii)===== Find the multiplicative inverse of the fol
- Question 7, Exercise 2.3
- given matrices \(A\) and \(B\). =====Question 7(ii)===== Verify that $(A B)^{-1}=B^{-1} A^{-1}$ in e... . ** Solution. ** Do yourself. =====Question 7(iii)===== Verify that $(A B)^{-1}=B^{-1} A^{-1}$ in