Worksheet on Understanding Matrix

Practice the questions given in the Worksheet on understanding matrix.

1. For the matrix A = \(\begin{bmatrix} 6 & 13\\ -5 & -7\\ 2 & 4 \end{bmatrix}\), answer the following.

(i) What is the order of the matrix A?

(ii) Find the (2, 1)th, (1, 2)th and (3, 2)th elements.

(iii) Is it a rectangular matrix or a square matrix?

2. (i) A matrix has 4 elements. Write the possible orders of the matrix.

(ii) A matrix has 11 elements. Write the possible orders of the matrix.

(iii) A matrix has 3 rows and 2 columns, what is the number of elements in the matrix?

3. (i) If \(\begin{bmatrix} 10 & x\\ -5 & 2 \end{bmatrix}\) = \(\begin{bmatrix} 10 & 1\\ -5 & 2 \end{bmatrix}\), Find the value of x.

(ii) If \(\begin{bmatrix} 1 & a + b\\ -4 & 3\\ a - b & 2 \end{bmatrix}\) = \(\begin{bmatrix} 1 & -2\\ -4 & 3\\ 1 & 2 \end{bmatrix}\), find a and b.

(iii) If \(\begin{bmatrix} 2x + y & 1\\ 3 & x – 3y \end{bmatrix}\) = \(\begin{bmatrix} 1 & 1\\ 3 & 2 \end{bmatrix}\), Find the value of x and y.

Answers for the Worksheet on Understanding Matrix are given below.

Answers

1. (i) The order of the matrix A is 3 × 2.

(ii) (2, 1)th element = -5;

     (1, 2)th element = 13;

     (3, 2)th element = 4.

(iii) The matrix A has 3 rows and 2 columns. The number of rows ≠ the number of columns. Therefore the matrix A is rectangular matrix.

2. (i) The possible orders of the matrix are: 1 × 4; 4 × 1 and 2 × 2.

(ii) The possible orders of the matrix are: 11 × 1 and 1 × 11.

(iii) The number of elements in the matrix = 3 × 2 = 6.

3. (i) The value of x = 1

(ii)  The value of a = -½ and b = -\(\frac{3}{2}\)

(iii) The value of x = \(\frac{5}{7}\) and y = -\(\frac{3}{7}\).

10th Grade Math

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