Here we will solve different types of Problems on classification of matrices
1. Let A = \(\begin{bmatrix} -5\\3\\ 2 \end{bmatrix}\), B = \(\begin{bmatrix} 8 & 1\\ -6 & 7 \end{bmatrix}\), C = \(\begin{bmatrix} 6 & 7 & -4\\ -1 & 1 & 2\\ 3 & 0 & 5 \end{bmatrix}\),
X = \(\begin{bmatrix} 3 & 6\\ -2 & 7\\ 0 & 1 \end{bmatrix}\), Y = \(\begin{bmatrix} 8 & 0 & -4 \end{bmatrix}\).
Indicate the class of each of the matrices.
Solution:
A = \(\begin{bmatrix} -5\\3\\ 2 \end{bmatrix}\)
A is a column matrix, because it has exactly one column.
B = \(\begin{bmatrix} 8 & 1\\ -6 & 7 \end{bmatrix}\)
B is a square matrix, because number of rows = number of columns = 2
C = \(\begin{bmatrix} 6 & 7 & -4\\ -1 & 1 & 2\\ 3 & 0 & 5 \end{bmatrix}\)
C is a square matrix, because number of rows = number of
columns = 3.
X = \(\begin{bmatrix} 3 & 6\\ -2 & 7\\ 0 & 1 \end{bmatrix}\)
X is a rectangular matrix, because number of rows ≠ number of columns.
Y = \(\begin{bmatrix} 8 & 0 & -4 \end{bmatrix}\)
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:
A null matrix of the order 2 × 3 is \(\begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}\).
A unit matrix of the order 3 × 3 is \(\begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}\).
Practice Problems on Classification of Matrices:
1. let A = [8 -7 5], B = \(\begin{bmatrix} 1 & -5\\ 3 & 7 \end{bmatrix}\), C = \(\begin{bmatrix} 2 & 1 & 6\\ 1 & 0 & 5\\ 3 & 1 & 1 \end{bmatrix}\), M = \(\begin{bmatrix} 1 & 0\\ 0 & 1 \end{bmatrix}\) and N = \(\begin{bmatrix} 4 & -1\\ 2 & 0\\ 7 & -3 \end{bmatrix}\).
(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 \(\begin{bmatrix} 0 & 0 & 0\\ 0 & 0 & 0 \end{bmatrix}\)
(ii) 4 × 4 order unit matrix is \(\begin{bmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{bmatrix}\)
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