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The rank of a unit matrix of order n is
- a)1
- b)2
- c)0
- d)n
Correct answer is option 'D'. Can you explain this answer?
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The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is o...
The rank of a matrix refers to the maximum number of linearly independent rows or columns in the matrix. In other words, it is the number of non-zero rows or columns in the matrix when it is in its row echelon form or reduced row echelon form.
The unit matrix, also known as the identity matrix, is a special type of matrix with ones on the main diagonal and zeros elsewhere. For example, the unit matrix of order 3 is:
```
1 0 0
0 1 0
0 0 1
```
To determine the rank of a unit matrix of order n, we need to find the maximum number of linearly independent rows or columns in the matrix.
Let's consider a unit matrix of order n:
```
1 0 0 ... 0
0 1 0 ... 0
0 0 1 ... 0
. . . ... .
. . . ... .
. . . ... .
0 0 0 ... 1
```
Since each row or column in a unit matrix is linearly independent from each other, the maximum number of linearly independent rows or columns is equal to the order of the matrix, which is n.
Therefore, the rank of a unit matrix of order n is n, as mentioned in option 'D'.
The unit matrix, also known as the identity matrix, is a special type of matrix with ones on the main diagonal and zeros elsewhere. For example, the unit matrix of order 3 is:
```
1 0 0
0 1 0
0 0 1
```
To determine the rank of a unit matrix of order n, we need to find the maximum number of linearly independent rows or columns in the matrix.
Let's consider a unit matrix of order n:
```
1 0 0 ... 0
0 1 0 ... 0
0 0 1 ... 0
. . . ... .
. . . ... .
. . . ... .
0 0 0 ... 1
```
Since each row or column in a unit matrix is linearly independent from each other, the maximum number of linearly independent rows or columns is equal to the order of the matrix, which is n.
Therefore, the rank of a unit matrix of order n is n, as mentioned in option 'D'.
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The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer?.
The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer? for IIT JAM 2025 is part of IIT JAM preparation. The Question and answers have been prepared according to the IIT JAM exam syllabus. Information about The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for IIT JAM 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The rank of a unit matrix of order n isa)1b)2c)0d)nCorrect answer is option 'D'. Can you explain this answer?.
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