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 = -\(\frac{9}{2}\).

**From ****Problems on Understanding Matrices**** to HOME**

**Didn't find what you were looking for? Or want to know more information
about Math Only Math.
Use this Google Search to find what you need.**

## New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.