Search
You can find the results of your search below.
Fulltext results:
- Question 4, Exercise 2.3
- ====== Question 4, Exercise 2.3 ====== Solutions of Question 4 of Exercise 2.3 of Unit 02: Matrices and Det... & 5 & 6 & 7 \\9 & 10 & 11 & 12\end{bmatrix}$ ====Solution==== \begin{align}&\begin{bmatrix} 2 & 3 & 4 & 5
- Question 3, Exercise 2.3
- ====== Question 3, Exercise 2.3 ====== Solutions of Question 3 of Exercise 2.3 of Unit 02: Matrices and Det... \\ -1 & 2 & 3 \\ \end{matrix} \right]$$ ====Solution==== \begin{align}&\begin{bmatrix} 1 & 0 & -2 \\ ... \\ 1 & -1 & -2 \\ \end{matrix} \right]$$ ====Solution==== \begin{align}&\begin{bmatrix} 3 & 1 & -4 \\
- Question 2, Exercise 2.3
- ====== Question 2, Exercise 2.3 ====== Solutions of Question 2 of Exercise 2.3 of Unit 02: Matrices and Det... \\ 2 & 1 & 0 \\ -1 & 2 & 3 \end{bmatrix}$$ ====Solution==== Let $$A=\begin{bmatrix} 4 & -2 & 5 \\ 2 & 1 ... \\ -1 & 5 & 1 \\ \end{matrix} \right]$$ ====Solution==== Let $$A=\begin{bmatrix} 3 & -1 & 6 \\ 1 & 3 ... \\ -2 & -2 & 2 \\ \end{matrix} \right]$$ ====Solution==== Let $$A=\begin{bmatrix} 1 & 2 & -3 \\ 0 & -2
- Question 1, Exercise 2.3
- ====== Question 1, Exercise 2.3 ====== Solutions of Question 1 of Exercise 2.3 of Unit 02: Matrices and Det... -1 \\2 & 1 & 4 \\3 & 4 & -5\end{bmatrix}$. ====Solution==== \begin{align}&\begin{bmatrix} 1 & 3 & -1 \\ ... d 1 & 3 & \quad 2\end{bmatrix} \end{align}$. ====Solution==== \begin{align} &\begin{bmatrix} 2 & 3 & -1 & 9... & 1 \\1 & 1 & 2 \\4 & 1 & 7\end{bmatrix}$. ====Solution==== \begin{align}&\begin{bmatrix} 2 & -3 & 1 \\
- Question 11, Exercise 2.2
- ====== Question 11, Exercise 2.2 ====== Solutions of Question 11 of Exercise 2.2 of Unit 02: Matrices and D... \6 & 2 & -2 \\5 & 1 & 1\end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 7 & 1 & 3 \... & -2 & 1 \\-2 & -3 & 2 \end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 1 & -1 & 1 ... & 6 & -3 \\-1 & 0 & 1 \end{matrix} \right]$ ====Solution==== Let $$A=\left[ \begin{matrix} 3 & 2 & -3
- Question 8,9 & 10, Exercise 2.2
- ====== Question 8,9 & 10, Exercise 2.2 ====== Solutions of Questions 8,9 & 10 of Exercise 2.2 of Unit 02: M... \\x & y & 1+z \end{matrix} \right|=1+x+y+z$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1+x & y... \end{matrix} \right|=( x-p )( x-q )( x+p+q )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} x & p &... ( 1+\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c} )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1+a & 1
- Question 7, Exercise 2.2
- ====== Question 7, Exercise 2.2 ====== Solutions of Question 7 of Exercise 2.2 of Unit 02: Matrices and Det... 0 & 3861 \\3862 & 3863 \end{matrix} \right|$ ====Solution==== Given $$\left| \begin{matrix} 3860 & 3861 ... 85 & 86 \\87 & 88 & 89\end{matrix} \right|$ ====Solution==== Given $$\left| \begin{matrix} 81 & 82 & 83
- Question 6, Exercise 2.2
- ====== Question 6, Exercise 2.2 ====== Solutions of Question 6 of Exercise 2.2 of Unit 02: Matrices and Det... b \\c-a & a-b & b-c \end{matrix} \right|=0$ ====Solution==== Let \begin{align} L.H.S&=\left| \begin{matrix... trix} \right|=( a-b )( b-c )( c-a )( a+b+c )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1 & a &... \end{matrix} \right|=( a-b )( b-c )( c-a )$ ====Solution==== Let $$L.H.S.=\left| \begin{matrix} 1 & a &
- Question 5, Exercise 2.2
- ====== Question 5, Exercise 2.2 ====== Solutions of Question 5 of Exercise 2.2 of Unit 02: Matrices and Det... & l & x\\b & m & y\\c & n & z \end{vmatrix}$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} a & b & ... & b & c\\1 & 2 & 3\\4 & 5 & 6 \end{vmatrix}.$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} a & b & ... c \\b+c & c+a & a+b \end{matrix} \right|=0$ ====Solution==== \begin{align}L.H.S.&=\begin{vmatrix} 1 & 1 &
- Question 4, Exercise 2.2
- ====== Question 4, Exercise 2.2 ====== Solutions of Question 4 of Exercise 2.2 of Unit 02: Matrices and Det... 1 & 2 & 1 \\2 & 1 & 1 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 0 & 1 ... & 4 & -6 \\4 & 2 & 0 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 3 & 4 ... -5 & 4 \\-9 & 8 & -7 \end{matrix} \right|.$ ====Solution==== \begin{align}&\left| \begin{matrix} 3 & 1
- Question 3, Exercise 2.2
- ====== Question 3, Exercise 2.2 ====== Solutions of Question 3 of Exercise 2.2 of Unit 02: Matrices and Det... x of order $3,$ then verify that $|A^t|=|A|$. ====Solution==== Let $$A=\begin{bmatrix} a_{11} & a_{12} &
- Question 19, Exercise 2.2
- ====== Question 19, Exercise 2.2 ====== Solutions of Question 19 of Exercise 2.2 of Unit 02: Matrices and D... ix}$. Verify that $( A^{-1})^t=( A^t)^{-1}$ . ====Solution==== Given $$A=\left[ \begin{matrix} 2 & 3 \\
- Question 2, Exercise 2.2
- ====== Question 2, Exercise 2.2 ====== Solutions of Question 2 of Exercise 2.2 of Unit 02: Matrices and Det... & 1 & 0 \\-1 & 2 & 0 \end{matrix}\right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 & 0 \... & -12 \\2 & -1 & 3 \end{matrix} \right|=0$. ====Solution==== Given $$\left| \begin{matrix} 1 & 2 & 3 \... & -1 & 1 \\-2 & 1 & 4 \end{matrix} \right|$. ====Solution==== Given $$\left| \begin{matrix} 1 & 3 & -2
- Question 16 & 17, Exercise 2.2
- ====== Question 16 & 17, Exercise 2.2 ====== Solutions of Questions 16 & 17 of Exercise 2.2 of Unit 02: Mat... atrix}$. Show that $|A^{-1}|=\dfrac{1}{|A|}$. ====Solution==== Given $$A=\left[ \begin{matrix} 3 & -1 \\... egin{bmatrix} -1 & 1 \\2 & 3\end{bmatrix}$. ====Solution==== Given $$A=\left[ \begin{matrix} 2 & 3 \\
- Question 18, Exercise 2.2
- ====== Question 18, Exercise 2.2 ====== Solutions of Question 18 of Exercise 2.2 of Unit 02: Matrices and D... matrices, then show that $( A^{-1})^{-1}=A$. ====Solution==== Let $A$ is $2\times 2$ non-singular matrix.\\... es, then show that $( AB )^{-1}=B^{-1}A^{-1}$ ====Solution==== Let $A$ and $B$ are $2\times 2$ non-singular