Consider following statements:
1) Every zero matrix is a square matrix.
2) A matrix has a numerical value.
3) A unit matrix is a diagonal matrix.
Which of the above statements is/are correct?
A) 2 only
B) 3 only
C) 2 and 3 only
Answer
635.7k+ views
Hint:
First we will get what is zero matrix, square matrix, unit matrix and diagonal matrix. Then we will see which statement is true according to their definitions.
Complete step by step solution:
Zero matrix: It is the matrix with all elements zero. It is also called null matrix. But it is not necessarily a square matrix. It can be of dimensions \[m \times n\] or \[n \times n\]. Where m is the number of rows and m is the number of columns.
\[\left( {\begin{array}{*{20}{c}}
0&0 \\
0&0
\end{array}} \right)\] or \[\left( {\begin{array}{*{20}{c}}
0 \\
0 \\
0
\end{array}\begin{array}{*{20}{c}}
0 \\
0 \\
0
\end{array}} \right)\] both are zero matrices.
Square matrix: It is the matrix having the same number of rows and columns. That is having dimensions \[n \times n\].
Unit matrix: It is the matrix whose diagonal elements are 1 and rest other elements are zero. It is also called identity matrix.
\[\left( {\begin{array}{*{20}{c}}
1&0 \\
0&1
\end{array}} \right)\]
Diagonal matrix: It is the matrix with only diagonal elements present, the rest other are zero.
From these definitions it is clear that statement 1 is false but statement 3 is true.
Now about statement 2 we can say that a matrix is not having value; whereas it is a determinant that has a value. So statement 2 is also false.
Thus option B is the correct option.
Note:
Students note that matrices need not to be square always. Their dimensions may vary. Also note that every unit matrix is a diagonal matrix but not the reverse case is true always. We can have mathematical operations with matrices.
First we will get what is zero matrix, square matrix, unit matrix and diagonal matrix. Then we will see which statement is true according to their definitions.
Complete step by step solution:
Zero matrix: It is the matrix with all elements zero. It is also called null matrix. But it is not necessarily a square matrix. It can be of dimensions \[m \times n\] or \[n \times n\]. Where m is the number of rows and m is the number of columns.
\[\left( {\begin{array}{*{20}{c}}
0&0 \\
0&0
\end{array}} \right)\] or \[\left( {\begin{array}{*{20}{c}}
0 \\
0 \\
0
\end{array}\begin{array}{*{20}{c}}
0 \\
0 \\
0
\end{array}} \right)\] both are zero matrices.
Square matrix: It is the matrix having the same number of rows and columns. That is having dimensions \[n \times n\].
Unit matrix: It is the matrix whose diagonal elements are 1 and rest other elements are zero. It is also called identity matrix.
\[\left( {\begin{array}{*{20}{c}}
1&0 \\
0&1
\end{array}} \right)\]
Diagonal matrix: It is the matrix with only diagonal elements present, the rest other are zero.
From these definitions it is clear that statement 1 is false but statement 3 is true.
Now about statement 2 we can say that a matrix is not having value; whereas it is a determinant that has a value. So statement 2 is also false.
Thus option B is the correct option.
Note:
Students note that matrices need not to be square always. Their dimensions may vary. Also note that every unit matrix is a diagonal matrix but not the reverse case is true always. We can have mathematical operations with matrices.
Recently Updated Pages
10 examples of friction in our daily life

Write structures of the following compounds i 2 Chloro3methylpentane class 11 chemistry CBSE

What is BLO What is the full form of BLO class 8 social science CBSE

Explain the Treaty of Vienna of 1815 class 10 social science CBSE

A Paragraph on Pollution in about 100-150 Words

XIX+XXX A 49 B 51 C 55 D 44 class 5 maths CBSE

Trending doubts
Find the value of the expression given below sin 30circ class 11 maths CBSE

What do you mean by retardation What is its SI uni class 11 physics CBSE

Draw a diagram of nephron and explain its structur class 11 biology CBSE

Difference between physical and chemical change class 11 chemistry CBSE

Draw a labelled diagram of the neuron and describe class 11 biology CBSE

What are derived physical quantities Give any two examples class 11 physics CBSE

