Search
You can find the results of your search below.
Matching pagenames:
- 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 an... & 1 & 0 \\-1 & 2 & 0 \end{matrix}\right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 &... & -12 \\2 & -1 & 3 \end{matrix} \right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 &... & -1 & 1 \\-2 & 1 & 4 \end{matrix} \right|$. ====Solution==== Given $$\left| \begin{matrix} 1 & 3 &
- Question 13, Exercise 2.2
- ====== Question 13, Exercise 2.2 ====== Solutions of Question 13 of Exercise 2.2 of Unit 02: Matrices ... BB) Peshawar, Pakistan. =====Question 13(i)===== Solve for $x,$ $\left| \begin{matrix}x & 2 & 3 \\0 & -1 & 1 \\0 & 4 & 5 \end{matrix} \right|=9$ ====Solution==== Given $$\left| \begin{matrix} x & 2 &... $ $$-9x=9$$ $$x=-1$$ =====Question 13(ii)===== Solve for $x,$ $\left| \begin{matrix}-1 & 0 & 1 \\x
- Question 5 & 6, Exercise 2.1
- ====== Question 5 & 6, Exercise 2.1 ====== Solutions of Question 5 & 6 of Exercise 2.1 of Unit 02: Mat... be symmetric. Find the value of $a$ and $b$. ====Solution==== Given: $A=\begin{bmatrix} 0 & 2b & -2 \... and } b=\dfrac{3}{2}.$$ =====Question 6(i)===== Solve the matrix equations for $X.$ Find $X-3A=2B$, i... trix}2 & 1 & 1 \\ 3 & -1 & 4 \end{bmatrix}$. ====Solution==== Given $A=\left[ \begin{matrix} 1 & 0 &
- Question 6, Exercise 2.2
- ====== Question 6, Exercise 2.2 ====== Solutions of Question 6 of Exercise 2.2 of Unit 02: Matrices an... b \\c-a & a-b & b-c \end{matrix} \right|=0$ ====Solution==== Let \begin{align} L.H.S&=\left| \begin{m... trix} \right|=( a-b )( b-c )( c-a )( a+b+c )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1 ... \end{matrix} \right|=( a-b )( b-c )( c-a )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1
- Question 4, Exercise 2.2
- ====== Question 4, Exercise 2.2 ====== Solutions of Question 4 of Exercise 2.2 of Unit 02: Matrices an... 1 & 2 & 1 \\2 & 1 & 1 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 0... & 4 & -6 \\4 & 2 & 0 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 3... -5 & 4 \\-9 & 8 & -7 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 3
- Question 5, Exercise 2.2
- ====== Question 5, Exercise 2.2 ====== Solutions of Question 5 of Exercise 2.2 of Unit 02: Matrices an... & l & x\\b & m & y\\c & n & z \end{vmatrix}$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} a &... & b & c\\1 & 2 & 3\\4 & 5 & 6 \end{vmatrix}.$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} a &... c \\b+c & c+a & a+b \end{matrix} \right|=0$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} 1 &
- Question 3, Exercise 2.1
- ====== Question 3, Exercise 2.1 ====== Solutions of Question 3 of Exercise 2.1 of Unit 02: Matrices an... that $\left( AB \right)C=A\left( BC \right)$. ====Solution==== Given: $A=\begin{bmatrix}x & y & z\end{b... \end{bmatrix}$. Verify that $A(B+C)=AB+AC$. ====Solution==== Given: $A=\begin{bmatrix} 1 & 3 \\ -1 &... \end{bmatrix}.$ Verify that $A( B-C )=AB-AC$. ====Solution==== Given: $ A=\begin{bmatrix}1 & 3 \\-1 &
- Question 8,9 & 10, Exercise 2.2
- ====== Question 8,9 & 10, Exercise 2.2 ====== Solutions of Questions 8,9 & 10 of Exercise 2.2 of Unit ... \\x & y & 1+z \end{matrix} \right|=1+x+y+z$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1+... \end{matrix} \right|=( x-p )( x-q )( x+p+q )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} x ... ( 1+\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1+
- Question 11, Exercise 2.2
- ====== Question 11, Exercise 2.2 ====== Solutions of Question 11 of Exercise 2.2 of Unit 02: Matrices ... \6 & 2 & -2 \\5 & 1 & 1\end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 7 & 1 &... & -2 & 1 \\-2 & -3 & 2 \end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 1 & -1 ... & 6 & -3 \\-1 & 0 & 1 \end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 3 & 2 &
- Question 1, Exercise 2.1
- ====== Question 1, Exercise 2.1 ====== Solutions of Question 1 of Exercise 2.1 of Unit 02: Matrices an... rix} 2 \\ 4 \\ 6 \\ \end{matrix} \right]$$ ====Solution==== \begin{align}&\left[ \begin{matrix} 1... ix} 2 & -5 & 7 \\ \end{matrix} \right]$$ ====Solution==== \begin{align}&\left[ \begin{matrix} 1... ix} 4 \\ 2 \\ \end{matrix} \right]$$ ====Solution==== \begin{align}&\left[ \begin{matrix} 7
- Question 8, Exercise 2.1
- ====== Question 8, Exercise 2.1 ====== Solutions of Question 8 of Exercise 2.1 of Unit 02: Matrices an... & 4 \end{bmatrix}$, show that $( A^t )^t=A$. ====Solution==== Given $$A=\left[ \begin{matrix} 1 & 2... & 4\end{bmatrix}$, show that $AA^t\ne A^tA$. ====Solution==== $$A=\left[ \begin{matrix} 1 & 2 & 0 ... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p6 |< Question 7]]</btn></text> <tex
- Question 9, Exercise 2.1
- ====== Question 9, Exercise 2.1 ====== Solutions of Question 9 of Exercise 2.1 of Unit 02: Matrices an... \end{bmatrix}$, show that $( AB )^t=B^tA^t$. ====Solution==== $$A=\left[ \begin{matrix} 2 & -1 & 3... 2 \end{bmatrix}$, show that $( AB)^t=B^tA^t$. ====Solution==== $$A=\left[ \begin{matrix} \quad 1 & ... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p7 |< Question 8]]</btn></text> <tex
- Question 12, Exercise 2.1
- ====== Question 12, Exercise 2.1 ====== Solutions of Question 12 of Exercise 2.1 of Unit 02: Matrices ... d{bmatrix}$. Verify that$A+A^t$ is symmetric. ====Solution==== $$A=\left[ \begin{matrix} 3 & 2 & 1 ... trix}$. Verify that$A-A^t$ is skew symmetric. ====Solution==== $$A=\left[ \begin{matrix} 3 & 2 & 1 ... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-1-p10 |< Question 11]]</btn></text> <t
- Question 7, Exercise 2.2
- ====== Question 7, Exercise 2.2 ====== Solutions of Question 7 of Exercise 2.2 of Unit 02: Matrices an... 0 & 3861 \\3862 & 3863 \end{matrix} \right|$ ====Solution==== Given $$\left| \begin{matrix} 3860 & ... 85 & 86 \\87 & 88 & 89\end{matrix} \right|$ ====Solution==== Given $$\left| \begin{matrix} 81 & 82... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-2-p6 |< Question 6]]</btn></text> <tex
- Question 14 & 15, Exercise 2.2
- ====== Question 14 & 15, Exercise 2.2 ====== Solutions of Questions 14 & 15 of Exercise 2.2 of Unit 02... e of square matrix exists. Then it is unique. ====Solution==== =====Question 15===== Let $A=\beg... 2 \\1 & 0 & 5\end{bmatrix}$. Find $A^{-1}$. ====Solution==== Given $$A=\left[ \begin{matrix} 0 & 2... xt align="left"><btn type="primary">[[math-11-kpk:sol:unit02:ex2-2-p11 |< Question 13]]</btn></text> <t