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A diagonal matrix in which all the diagonal elements are equal is a ______________.
-
- a)scalar matrix.
- b)column matrix.
- c)unit matrix.
- d)None
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A diagonal matrix in which all the diagonal elements are equal is a __...
Correct answer: (A)
scalar matrix.
scalar matrix.
Most Upvoted Answer
A diagonal matrix in which all the diagonal elements are equal is a __...
Diagonal Matrix:
A diagonal matrix is a square matrix in which all the non-diagonal elements are zero. In other words, a diagonal matrix is a matrix in which all the elements outside the main diagonal are zero.
Equal Diagonal Elements:
In this question, it is mentioned that all the diagonal elements of the matrix are equal. The diagonal elements of a matrix are the elements that lie on the main diagonal, which extends from the top left corner to the bottom right corner of the matrix.
Scalar Matrix:
A scalar matrix is a special type of diagonal matrix in which all the diagonal elements are equal. In other words, a scalar matrix is a diagonal matrix in which all the non-zero elements are the same.
Explanation:
In this question, it is mentioned that all the diagonal elements of the matrix are equal. This means that the matrix satisfies the condition of a scalar matrix, which is a special type of diagonal matrix.
A scalar matrix is a square matrix in which all the diagonal elements are equal. It can be represented as follows:
```
[a 0 0]
[0 a 0]
[0 0 a]
```
In the above representation, 'a' represents the common value of all the diagonal elements. Since the given matrix satisfies this condition, it can be classified as a scalar matrix.
Conclusion:
Therefore, the correct answer is option A, a scalar matrix.
A diagonal matrix is a square matrix in which all the non-diagonal elements are zero. In other words, a diagonal matrix is a matrix in which all the elements outside the main diagonal are zero.
Equal Diagonal Elements:
In this question, it is mentioned that all the diagonal elements of the matrix are equal. The diagonal elements of a matrix are the elements that lie on the main diagonal, which extends from the top left corner to the bottom right corner of the matrix.
Scalar Matrix:
A scalar matrix is a special type of diagonal matrix in which all the diagonal elements are equal. In other words, a scalar matrix is a diagonal matrix in which all the non-zero elements are the same.
Explanation:
In this question, it is mentioned that all the diagonal elements of the matrix are equal. This means that the matrix satisfies the condition of a scalar matrix, which is a special type of diagonal matrix.
A scalar matrix is a square matrix in which all the diagonal elements are equal. It can be represented as follows:
```
[a 0 0]
[0 a 0]
[0 0 a]
```
In the above representation, 'a' represents the common value of all the diagonal elements. Since the given matrix satisfies this condition, it can be classified as a scalar matrix.
Conclusion:
Therefore, the correct answer is option A, a scalar matrix.
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A diagonal matrix in which all the diagonal elements are equal is a ______________. a)scalar matrix.b)column matrix.c)unit matrix.d)NoneCorrect answer is option 'A'. Can you explain this answer?
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