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Problems on Classification of Matrices

Here we will solve different types of Problems on classification of matrices

1. Let A = [532], B = [8167], C = [674112305],

X = [362701], Y = [804].

Indicate the class of each of the matrices.

Solution:

A = [532]

A is a column matrix, because it has exactly one column.


B = [8167]

B is a square matrix, because number of rows = number of columns = 2


C = [674112305]

3 × 3 Order Square Matrix

C is a square matrix, because number of rows = number of columns = 3.


X = [362701]

3 × 2 Rectangular Matrix

X is a rectangular matrix, because number of rows ≠ number of columns.


Y = [804]

Y is a row matrix, because it has exactly one row.


2. Construct a null matrix of the order 2 × 3 and a unit matrix of the order 3 × 3.

Solution:

Null Matrices

A null matrix of the order 2 × 3 is [000000].

A unit matrix of the order 3 × 3 is [000000000].


Practice Problems on Classification of Matrices:

1. let A = [8     -7     5], B = [1537], C = [216105311], M = [1001] and N = [412073].

(i) Identify the rectangular matrices.

(ii) Identify the square matrices.

(iii) Identify the row matrices and the column matrices.

Answer:

(i) A and N are the rectangular matrices.

(ii) B, C and M are the square matrices.

(iii) A is the row matrix; and there is no column matrix.


2. (i) Constant the 2 × 3 zero matrix.

(ii) Constant the 4 × 4 unit matrix.

Answer:

(i) 2 × 3 order zero matrix is [000000]

(ii) 4 × 4 order unit matrix is [1000010000100001]






10th Grade Math

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