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- Question 1, Exercise 2.1
- Question 2, Exercise 2.1
- Question 3, Exercise 2.1
- Question 4, Exercise 2.1
- Question 5 & 6, Exercise 2.1
- Question 7, Exercise 2.1
- Question 8, Exercise 2.1
- Question 9, Exercise 2.1
- Question 10, Exercise 2.1
- Question 11, Exercise 2.1
- Question 12, Exercise 2.1
- Question 13, Exercise 2.1
- Question 1, Exercise 2.2
- Question 2, Exercise 2.2
- Question 3, Exercise 2.2
- Question 4, Exercise 2.2
- Question 5, Exercise 2.2
- Question 6, Exercise 2.2
- Question 7, Exercise 2.2
- Question 8,9 & 10, Exercise 2.2
- Question 11, Exercise 2.2
- Question 12, Exercise 2.2
- Question 13, Exercise 2.2
- Question 14 & 15, Exercise 2.2
- Question 16 & 17, Exercise 2.2
- Question 18, Exercise 2.2
- Question 19, Exercise 2.2
- Question 1, Exercise 2.3
- Question 2, Exercise 2.3
- Question 3, Exercise 2.3
- Question 4, Exercise 2.3
Fulltext results:
- Question 2, Exercise 2.2
- ====== Question 2, Exercise 2.2 ====== Solutions of Question 2 of Exercise 2.2 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Without evaluating state the reasons fo... Because elements of third column are zero. =====Question 2(ii)===== Without evaluating state the reasons
- Question 4, Exercise 2.2
- ====== Question 4, Exercise 2.2 ====== Solutions of Question 4 of Exercise 2.2 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 4(i)===== Evaluate the determinant $\left| \begi... ft( -1-4 \right)\\ =&0+3-15=-12 \end{align} =====Question 4(ii)===== Evaluate the determinant $\left| \begi
- Question 5, Exercise 2.2
- ====== Question 5, Exercise 2.2 ====== Solutions of Question 5 of Exercise 2.2 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5(i)===== Show that $\begin{vmatrix}a & b & c\\l ... & n & z \end{vmatrix} =R.H.S. \end{align} =====Question 5(ii)===== Show that $\begin{vmatrix}a & b & c\\1
- Question 6, Exercise 2.2
- ====== Question 6, Exercise 2.2 ====== Solutions of Question 6 of Exercise 2.2 of Unit 02: Matrices and Determinants. This ... quad R_1 \cong R_3 \\ &=R.H.S. \end{align} =====Question 6(ii)===== Prov that $\left| \begin{matrix}1 & a ... -b )( b-c )( c-a )( a+b+c )$$ $$=R.H.S. $$ =====Question 6(iii)===== Prov that $\left| \begin{matrix}1 & a
- Question 2, Exercise 2.3
- ====== Question 2, Exercise 2.3 ====== Solutions of Question 2 of Exercise 2.3 of Unit 02: Matrices and Determinants. This ... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 2(i)===== Find the inverse of the matrix by using... 0 \\ 5 & -6 & 8 \end{bmatrix} \end{align} =====Question 2(ii)===== Find the inverse of the matrix by usin
- Question 1, Exercise 2.1
- ====== Question 1, Exercise 2.1 ====== Solutions of Question 1 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 1(i)===== Express as a single matrix $$\left[ \b... [ 14+20+64 \right]\\ &=[98].\end{align} =====Question 1(ii)===== Express as a single matrix $$\left[ \
- Question 3, Exercise 2.1
- ====== Question 3, Exercise 2.1 ====== Solutions of Question 3 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 3(i)===== If $A=\begin{bmatrix}x & y & z\end{bmat... From (1) and (2), we have $$(AB)C=A(BC).$$ =====Question 3(ii)(a)===== If $A=\begin{bmatrix}1 & 3 \\ -1 &
- Question 5 & 6, Exercise 2.1
- ====== Question 5 & 6, Exercise 2.1 ====== Solutions of Question 5 & 6 of Exercise 2.1 of Unit 02: Matrices and Determinant... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 5===== Matrix $A= \begin{bmatrix} 0 & 2b & -2 \\... dfrac{2}{3} \text{ and } b=\dfrac{3}{2}.$$ =====Question 6(i)===== Solve the matrix equations for $X.$ Fin
- Question 11, Exercise 2.2
- ====== Question 11, Exercise 2.2 ====== Solutions of Question 11 of Exercise 2.2 of Unit 02: Matrices and Determinants. Thi... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 11(i)===== Identify singular and non-singular mat... $ $$=28-16-12$$ $$|A|=0$$ $A$ is singular. =====Question 11(ii)===== Identify singular and non-singular ma
- Question 13, Exercise 2.2
- ====== Question 13, Exercise 2.2 ====== Solutions of Question 13 of Exercise 2.2 of Unit 02: Matrices and Determinants. Thi... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 13(i)===== Solve for $x,$ $\left| \begin{matrix}x... $x(-5-4)-2(0)+3(0)=9$$ $$-9x=9$$ $$x=-1$$ =====Question 13(ii)===== Solve for $x,$ $\left| \begin{matrix
- Question 8, Exercise 2.1
- ====== Question 8, Exercise 2.1 ====== Solutions of Question 8 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8(i)===== If $A=\begin{bmatrix}1 & 2 & 0 \\3 & -... \right]\\ \implies( A^t)^t&=A. \end{align} =====Question 8(ii)===== If $A=\begin{bmatrix}1 & 2 & 0\\3 & -1
- Question 9, Exercise 2.1
- ====== Question 9, Exercise 2.1 ====== Solutions of Question 9 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 9(i)===== If $A=\begin{bmatrix}2 & -1 & 3 \\1 & ... \end{matrix} \right]$$ $$( AB)^t=B^tA^t$$ =====Question 9(ii)===== If $A= \begin{bmatrix}\quad 1 & 2 & 0
- Question 12, Exercise 2.1
- ====== Question 12, Exercise 2.1 ====== Solutions of Question 12 of Exercise 2.1 of Unit 02: Matrices and Determinants. Thi... k Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 12(i)===== Let $A=\begin{bmatrix}3 & 2 & 1 \\4 &... matrix} \right]$$ $$( A+A^t )^t=( A+A^t )$$ =====Question 12(ii)===== Let $A=\begin{bmatrix}3 & 2 & 1 \\ 4
- Question 7, Exercise 2.2
- ====== Question 7, Exercise 2.2 ====== Solutions of Question 7 of Exercise 2.2 of Unit 02: Matrices and Determinants. This ... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 7(i)===== Evaluate $\left| \begin{matrix}3860 & 3... rix} \right|=14911180-14911182$$ $$=-2$$ =====Question 7(ii)===== Evaluate $\left| \begin{matrix}81 & 82
- Question 8,9 & 10, Exercise 2.2
- ====== Question 8,9 & 10, Exercise 2.2 ====== Solutions of Questions 8,9 & 10 of Exercise 2.2 of Unit 02: M... ok Board (KPTB or KPTBB) Peshawar, Pakistan. =====Question 8===== Prove that $\left| \begin{matrix}1+x & y &... z)-0-1(xy-x-xy)$$ $$=1+y+z+x$$ $$=R.H.S.$$ =====Question 9===== Prove that $\left| \begin{matrix}x & p & q... +q+p)$$ $$=(x-p)(x-q)(x+q+p)$$ $$=R.H.S.$$ =====Question 10===== Prove that $\left| \begin{matrix}1+a & 1