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A square matrix in which all the elements except at least the one element in the diagonal are zeros is said to be a
- a)identical matrix
- b)null/zero matrix
- c)column matrix
- d)diagonal matrix
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A square matrix in which all the elements except at least the one elem...
A diagonal matrix is a matrix in which all of the elements not on the diagonal of a square matrix are 0.
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A square matrix in which all the elements except at least the one elem...
Explanation:
A square matrix is a matrix in which the number of rows is equal to the number of columns. A diagonal matrix is a special type of square matrix in which all the non-diagonal elements are zero. The diagonal elements can be any real number, including zero.
Properties of Diagonal Matrix:
1. A diagonal matrix is always a square matrix.
2. All the elements of a diagonal matrix except those on the diagonal are zero.
3. The diagonal elements of a diagonal matrix need not be distinct.
4. The sum of two diagonal matrices is also a diagonal matrix.
5. The product of two diagonal matrices is also a diagonal matrix.
6. The inverse of a diagonal matrix is also a diagonal matrix, provided that all the diagonal elements are non-zero.
Uses of Diagonal Matrix:
1. Diagonal matrices are used in the field of linear algebra, particularly in the study of linear transformations.
2. Diagonal matrices are also used in the field of statistics, particularly in the study of covariance matrices.
3. Diagonal matrices are also used in the field of computer graphics, particularly in the representation of 3D objects.
Conclusion:
In summary, a diagonal matrix is a special type of square matrix in which all the non-diagonal elements are zero. The diagonal elements can be any real number, including zero. Diagonal matrices have special properties and are commonly used in various fields of mathematics and computer science.
A square matrix is a matrix in which the number of rows is equal to the number of columns. A diagonal matrix is a special type of square matrix in which all the non-diagonal elements are zero. The diagonal elements can be any real number, including zero.
Properties of Diagonal Matrix:
1. A diagonal matrix is always a square matrix.
2. All the elements of a diagonal matrix except those on the diagonal are zero.
3. The diagonal elements of a diagonal matrix need not be distinct.
4. The sum of two diagonal matrices is also a diagonal matrix.
5. The product of two diagonal matrices is also a diagonal matrix.
6. The inverse of a diagonal matrix is also a diagonal matrix, provided that all the diagonal elements are non-zero.
Uses of Diagonal Matrix:
1. Diagonal matrices are used in the field of linear algebra, particularly in the study of linear transformations.
2. Diagonal matrices are also used in the field of statistics, particularly in the study of covariance matrices.
3. Diagonal matrices are also used in the field of computer graphics, particularly in the representation of 3D objects.
Conclusion:
In summary, a diagonal matrix is a special type of square matrix in which all the non-diagonal elements are zero. The diagonal elements can be any real number, including zero. Diagonal matrices have special properties and are commonly used in various fields of mathematics and computer science.
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A square matrix in which all the elements except at least the one elem...
The matrix is said to be diagonal if its non diagonal elements are zero but diagonal elements may or may not be zero.
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A square matrix in which all the elements except at least the one element in the diagonal are zeros is said to be aa)identical matrixb)null/zero matrixc)column matrixd)diagonal matrixCorrect answer is option 'D'. Can you explain this answer?
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