Chapter 3 Matrices
- Find X, if Y = \(\left[\begin{array}{ll} 3 & 2 \\ 1 & 4 \end{array}\right]\) and 2X + Y = 2X + Y = [beginarrayll 1 & 0 \\ -3 & 2 endarray] ∴ 2X = [beginarrayll 1 & 0 \\ -3 & 2 endarray] – Y = [beginarrayll 1 & 0 \\ -3 & 2 endarray... 1
- Solve the equation for x, y, z and t, if, 2\(\left[\begin{array}{ll} x & z \\ y & t \end{array}\right]\) 2 [beginarrayll x & z \\ y & t endarray] +3 [beginarrayll 1 & -1 \\ 0 & 2 endarray] = 3 [beginarrayll 3 & 5 \\ 4 & 6 endarray] or [beginarra... 1
- If x\(\left[\begin{array}{l} 2 \\ 3 \end{array}\right]\) + y\(\left[\begin{array}{l} -1 \\ 1 \end{array}\right]\) x [beginarrayl 2 \\ 3 endarray] + y [beginarrayl -1 \\ 1 endarray] = [beginarrayl 10 \\ 5 endarray] . or [beginarrayl 2x \\ 3x endarray] + [... 1
- The bookshop of a particular school has 10 dozen chemistry books, 8 dozen physics books and 10 Let the number of books be represented by matrix A of order 1 x 3 as shown below : A = [10 dozen 8 dozen 10 dozen] = [120 96 120]. The cost... 1
- The restriction on n, k and p so that PY = WY will be defined are (A) k = 3, p = n (A) k = 3, p = n The order of matrix P is p x k and the order of matrix Y is 3 x k. PY is defined, when No. of columns in P = No. of rows in... 1
- If n = p, then the order of the matrix 7X – 5Z is (A) p x 2 (B) 2 x n (C) n x 3 (D) p x n (B) 2 x n The order of matrix X is 2 x n. The order of matrix Z is 2 x p. 7X – 5Z is defined when X and Z are of the same order. ⇒ n-p (give... 1
- In the matrix A = 2 5 19 -7 35 -2 5/2 12 (i) The order of the matrix = 3 x 4. (ii) Hie number of elements = 3 x 4 = 12. (iii) a13 = 19. a21 = 35, a33 = – 5, a24 = 12, a23 = 5 / 2 . 1
- If a matrix has 24 elements, what are possible orders it can have? What, if it has 13 elements? (i) 24 = 1 x 24 = 2 x 12 = 3 x 8 = 4 x 6 Thus, there are 8 matrices having 24 elements. Their orders are 1 x 24, 24 x 1, 2 x 12, 12 x 2, 3 x... 1
- If a matrix has 18 elements, what are the possible orders it can have? What, if it has 5 elements? (i) 18 = 1 x 18 = 2 x 9 = 3 x 6 There are 6 matrices of orders 1 x 18, 18 x 1, 2 x 9, 9 x 2, 3 x 6, 6 x 3. (ii) 5 = 1 x 5 There are two matr... 1
- Find the values of x, y and z from the following equations: (i) [beginarrayll 4 & 3 \\ x & 5 endarray] = [beginarrayll y & 3 \\ 1 & 5 endarray] Equating corresponding elements of the two matrices, we... 1
- Find the values of a, b, c and d from the equation \(\left[\begin{array}{cc} a-b & 3 a+c \end{array}\right]\) Comparing the corresponding elements of [beginarraycc a-b & 3 a+c \\ 2 a-b & 3 c+d endarray] = [beginarraycc -1 & 5 \\ 0 & 13 endarray] , we... 1
- A = [aij]mxn is a square matrix, if (A) m < n (B) m > n (C) m-n (D) None of these. For a square matrix m = n. 2
- The number of all possible matrices of order 3 x 3 with each entry 0 or 1 is (A) 27 (B) 18 (C) 81 (D) 512 There are 9 entries in a 3 x 3 matrix. Each place can be filled with 0 or 1. ∴ 9 places can be filled in 2⁹ = 512 ways. Number of such matri... 1