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- Question 1, Exercise 2.1
- \right]\\ &=[98].\end{align} =====Question 1(ii)===== Express as a single matrix $$\left[ \begin... \end{matrix} \right] \end{align} =====Question 1(iii)===== Express as a single matrix $$\left[ \begi
- Question 3, Exercise 2.1
- d (2), we have $$(AB)C=A(BC).$$ =====Question 3(ii)(a)===== If $A=\begin{bmatrix}1 & 3 \\ -1 & 4 \e... (2), we have $$A(B+C)=AB+AC.$$ =====Question 3(ii)(b)===== If $A=\begin{bmatrix} 1 & 3 \\ -1 & 4 \
- Question 2, Exercise 2.2
- ements of third column are zero. =====Question 2(ii)===== Without evaluating state the reasons for t... re identical, so result is zero. =====Question 2(iii)===== Without evaluating state the reasons for t
- Question 4, Exercise 2.2
- ight)\\ =&0+3-15=-12 \end{align} =====Question 4(ii)===== Evaluate the determinant $\left| \begin{mat... t) \\ =&36+96-80=52 \end{align} =====Question 4(iii)===== Evaluate the determinant $\left| \begin{ma
- Question 5, Exercise 2.2
- d{vmatrix} =R.H.S. \end{align} =====Question 5(ii)===== Show that $\begin{vmatrix}a & b & c\\1-3a &... end{vmatrix}=R.H.S. \end{align} =====Question 5(iii)===== Show that $\left| \begin{matrix}1 & 1 & 1
- Question 6, Exercise 2.2
- ong R_3 \\ &=R.H.S. \end{align} =====Question 6(ii)===== Prov that $\left| \begin{matrix}1 & a & a^3... ( c-a )( a+b+c )$$ $$=R.H.S. $$ =====Question 6(iii)===== Prov that $\left| \begin{matrix}1 & a & a^
- Question 11, Exercise 2.2
- 2$$ $$|A|=0$$ $A$ is singular. =====Question 11(ii)===== Identify singular and non-singular matrices... ero. Then $A$ is non-singular. =====Question 11(iii)===== Identify singular and non-singular matrice
- Question 13, Exercise 2.2
- )+3(0)=9$$ $$-9x=9$$ $$x=-1$$ =====Question 13(ii)===== Solve for $x,$ $\left| \begin{matrix}-1 & ... 1+x)=0$$ $$x=-1$$ $$x=0,-1$$ =====Question 13(iii)===== Solve for $x,$ $\left| \begin{matrix}x+2
- Question 1, Exercise 2.3
- 0 & -8 \end{bmatrix}\end{align} =====Question 1(ii)===== Reduce the matrices to the reduce echelon f... 1 & -1 \end{bmatrix}\end{align} ==== Question 1(iii) ==== Reduce the matrices to the reduce echelon
- Question 2, Exercise 2.3
- 6 & 8 \end{bmatrix} \end{align} =====Question 2(ii)===== Find the inverse of the matrix by using ele... & -7 & 5 \end{matrix} \right]$$ =====Question 2(iii)===== Find the inverse of the matrix by using el
- Question 5 & 6, Exercise 2.1
- end{matrix} \right]\end{align} =====Question 6(ii)===== Solve the matrix equations for $X.$ Find $2
- Question 8, Exercise 2.1
- \implies( A^t)^t&=A. \end{align} =====Question 8(ii)===== If $A=\begin{bmatrix}1 & 2 & 0\\3 & -1 & 4\
- Question 9, Exercise 2.1
- x} \right]$$ $$( AB)^t=B^tA^t$$ =====Question 9(ii)===== If $A= \begin{bmatrix}\quad 1 & 2 & 0 \\-1
- Question 12, Exercise 2.1
- ht]$$ $$( A+A^t )^t=( A+A^t )$$ =====Question 12(ii)===== Let $A=\begin{bmatrix}3 & 2 & 1 \\ 4 & 5 &
- Question 13, Exercise 2.1
- ht]$$ $$( A+A^t )^t=( A+A^t )$$ =====Question 13(ii)===== If $A$ is a square matrix of order $3$ then