Here we will solve different types of Problems on understanding matrices.
1. Let A = \(\begin{bmatrix} a & b\\ x & y \end{bmatrix}\). Answer the following.
(i) What is the order of the matrix A?
(ii) Find (2, 1)th and (1, 2)th elements.
Solution:
(i) The order is 2 × 2 because there are 2 rows and 2 columns in the matrix.
(ii) (2, 1)th element = the number falling in the 2^{nd} row and the 1^{st} column = x.
(1, 2)th element = the number falling in the 1^{st} row and the 2^{nd} column = b.
2. If a matrix has eight elements, find the possible orders of the matrix.
Solution:
8 = 8 × 1, 8 = 1 × 8, 8 = 2 × 4, 8 = 4 × 2.
Therefore, the possible orders of the matrix are 8 × 1, 1 × 8, 2 × 4 and 4 × 2.
3. In the matrix \(\begin{bmatrix} -10 & 4\\ 3 & 7\\ -1 & 5 \end{bmatrix}\), find the (2, 2)th, (3, 1)th and (1, 2)th elements.
Solution:
(2, 2)th element = the number falling in the 2^{nd} row and the 2^{nd} column = 7.
(3, 1)th element = the number falling in the 3^{rd} row and the 1^{st} column = -1.
(1, 2)th element = the number falling in the 1^{st} row and the 2^{nd} column = 4.
4. If A = B, where A = \(\begin{bmatrix} 3 & x + y\\ x - y & 5 \end{bmatrix}\) and B = \(\begin{bmatrix} 3 & -7\\ 2 & 5 \end{bmatrix}\) then find x and y.
Solution:
As A = B, the corresponding elements are equal. So, x + y = -7 and x – y = 2.
Adding the two equations we get, 2x = - 5.
Therefore, x = -\(\frac{5}{2}\).
Again, subtracting the 2^{nd} equation from the 1^{st} equation we get, 2y = -9.
Therefore, y = -\(\frac{9}{2}\).
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