Problems on Understanding Matrices

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 2nd row and the 1st column = x.

     (1, 2)th element = the number falling in the 1st row and the 2nd 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.

How to Find the Position of an Element in a Matrix?

Solution:

(2, 2)th element = the number falling in the 2nd row and the 2nd column = 7.

(3, 1)th element = the number falling in the 3rd row and the 1st column = -1.

(1, 2)th element = the number falling in the 1st row and the  2nd 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.

Equality of Matrices

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 2nd equation from the 1st equation we get, 2y = -9.

Therefore, y = -\(\frac{9}{2}\).






10th Grade Math

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.




Share this page: What’s this?

Recent Articles

  1. Worksheet on Addition of Mass | Word problems on Addition of Mass

    Nov 12, 24 02:22 PM

    Practice the third grade math worksheet on addition of mass/weight. This sheet provides different types of questions where you need to arrange the values of mass under different columns

    Read More

  2. Addition of Mass |Add the Different Units of Mass |Worked-out Examples

    Nov 12, 24 01:36 PM

    Adding Weight
    In addition of mass we will learn how to add the different units of mass or weight together. While adding we need to follow that the units of mass i.e., kilogram and gram are converted into grams

    Read More

  3. Measuring Mass | Addition and Subtraction of Mass | Measure of Mass

    Nov 12, 24 12:07 PM

    Measuring Mass
    We will discuss about measuring mass. We know the vegetable seller is weighing potatoes in kilogram. The goldsmith is weighing a ring in grams. The wheat bags are weighing in quintals.

    Read More

  4. Subtraction of Length | Learn How the Values of Length are Arranged

    Nov 11, 24 02:08 PM

    Subtraction of Length
    The process of subtraction of units of length is exactly similar to that of subtraction of ordinary numbers. Learn how the values of length are arranged in different columns for the subtraction of len…

    Read More

  5. Worksheet on Addition of Length | Word Problems on Addition of Length

    Nov 11, 24 01:52 PM

    Practice the third grade math worksheet on addition of length. This sheet provides different types of questions where you need to arrange the values of length under different columns to find their sum

    Read More