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- Exercise 2.2 (Solutions)
- given on this page. This exercise consists of the question related to sum, product and different operations on matrices. **Question 1.** Construct a matrix $A=\left[a_{i j}\right]$ ... {3}$\\ [[math-11-nbf:sol:unit02:ex2-2-p1|Solution:Question 1]] **Question 2.** Construct a matrix $B=\left[a_{\ell}\right]$ of order $3 \times 3$ for which:\\ (i) $b
- Exercise 2.3 (Solutions)
- given on this page. This exercise consists of the question related to determinant and inverse of the matrix. **Question. 1** Evaluate the determinant of the following ma... ht]$\\ [[math-11-nbf:sol:unit02:ex2-3-p1|Solution:Question 1]] **Question. 2** Evaluate the determinants of the following matrices using cofactor method.\\ (i) $\l
- Question 2, Exercise 2.1
- ====== Question 2, Exercise 2.1 ====== Solutions of Question 2 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 1(i)===== Identify the following matrix $\quad A=... rix.\\ ** Solution. ** Rectangular matrix =====Question 1(ii)===== Identify the following matrix $B=\left
- 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 ... deral Textbook Board, Islamabad, Pakistan. =====Question 4(i)===== Find $A$ if \begin{align}\left[\begin{a... rac{11}{2} \end{array}\right]. \end{align*} =====Question 4(ii)===== Find $X$ if $$\begin{bmatrix}3 & 2 \\
- Exercise 2.1 (Solutions)
- given on this page. This exercise consists of the question related to order, different type of matrices and transpose of matrix. **Question 1.** Find the order of the following matrix:\\ (i... t]$\\ [[math-11-nbf:sol:unit02:ex2-1-p1|Solution: Question 1]] **Question 2.** Identify the following matrices as square matrix, rectangular matrix, row matrix or co
- Question 1, Exercise 2.1
- ====== Question 1, Exercise 2.1 ====== Solutions of Question 1 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... al Textbook Board, Islamabad, Pakistan. ===== Question 1(i) ===== Find the order of the following matrix... text{Order of A}&= 2\times 3\end{align} ===== Question 1(ii) ===== Find the order of the following matri
- Question 4, Exercise 2.1
- ====== Question 4, Exercise 2.1 ====== Solutions of Question 4 of Exercise 2.1 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 4(i)===== Find the transpose of the following mat... & \sqrt{5} & 1 \\ 0 & 6 & 9 \end{bmatrix}$$ =====Question 4(ii)===== Find the transpose of the following ma
- Exercise 2.4 (Solutions)
- given on this page. This exercise consists of the question related to the determinant and properties of the determinant. **Question. 1** Without expansion show that: (i) $\left|\be... |=0$\\ [[math-11-nbf:sol:unit02:ex2-4-p1|Solution:Question 1(i-iv)]] **Question. 1** Without expansion show that:\\ (v) $\left|\begin{array}{lll}(a-b)^{3} & a^{3}-b^
- Question 1, Exercise 2.5
- ====== Question 1, Exercise 2.5 ====== Solutions of Question 1 of Exercise 2.5 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 1(i)===== First reduce each of the matrix into ec... 2 \end{align*} This is reduce echelon form. =====Question 1(ii)===== First reduce each of the matrix into e
- Review Exercise 2 (Solutions)
- this page. This exercise consists of the MCQs and question all topics included in this chapter. **Question 1.** Select the best matching option.\\ (i) If order of $A... hese\\ [[math-11-nbf:sol:unit02:Re-ex-p1|Solution:Question 1]] **Question 2.** For the matrix $A=\left[\begin{array}{ccc}1 & 2 & 0 \\ -3 & 4 & 9 \\ 2 & 1 & 6\end{arr
- 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 ... deral Textbook Board, Islamabad, Pakistan. =====Question 2(i)===== Evaluate the determinant of the follow... \\ 2 & 1 & 0 \end{array}\right]\) is: $-17$ =====Question 2(ii)===== Evaluate the determinant of the follo
- Question 3, Exercise 2.3
- ====== Question 3, Exercise 2.3 ====== Solutions of Question 3 of Exercise 2.3 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 3(i)===== Determine which of the matrix $\left[\b... = 0$, the matrix $A$ is a singular matrix. =====Question 3(ii)===== Determine which of the matrix $\left[\
- Question 4, Exercise 2.3
- ====== Question 4, Exercise 2.3 ====== Solutions of Question 4 of Exercise 2.3 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 4(i)===== Find the value of $\lambda$, so that th... nd{align*} Thus, $\lambda = \dfrac{16}{23}$. =====Question 4(ii)===== Find the value of $\lambda$, so that t
- Question 5, Exercise 2.3
- ====== Question 5, Exercise 2.3 ====== Solutions of Question 5 of Exercise 2.3 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 5(i)===== Find the multiplicative inverse of the ... 1}{9} & -\dfrac{1}{3} \end{array}\right]$$ =====Question 5(ii)===== Find the multiplicative inverse of the
- Question 2, Exercise 2.5
- ====== Question 2, Exercise 2.5 ====== Solutions of Question 2 of Exercise 2.5 of Unit 02: Matrices and Determinants. This ... deral Textbook Board, Islamabad, Pakistan. =====Question 2(i)===== Find the rank of each of the matrix $\l... ro rows.\\ The rank of the matrix is $3$. =====Question 2(ii)===== Find the rank of each of the matrix $\