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Types of Matrices - Matrices and Determinants, Business Mathematics & Statistics Video Lecture | Business Mathematics and Statistics - B Com
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FAQs on Types of Matrices - Matrices and Determinants, Business Mathematics & Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. What are the different types of matrices? |  |
Ans. There are several types of matrices, including:
- Square Matrix: A matrix with an equal number of rows and columns.
- Rectangular Matrix: A matrix with a different number of rows and columns.
- Diagonal Matrix: A square matrix where all the elements outside the main diagonal are zero.
- Identity Matrix: A square matrix with ones on the main diagonal and zeros elsewhere.
- Zero Matrix: A matrix where all the elements are zero.
| 2. How are square matrices different from rectangular matrices? | |
Ans. Square matrices have an equal number of rows and columns, whereas rectangular matrices have a different number of rows and columns. Square matrices have more symmetry and properties compared to rectangular matrices.
| 3. What is a diagonal matrix and what are its properties? | |
Ans. A diagonal matrix is a square matrix where all the elements outside the main diagonal are zero. The main diagonal is the line of elements from the top-left to the bottom-right of the matrix. The properties of a diagonal matrix include:
- The determinant of a diagonal matrix is equal to the product of its diagonal elements.
- The inverse of a diagonal matrix is obtained by taking the reciprocal of its diagonal elements.
- Multiplying a diagonal matrix by a scalar is equivalent to multiplying each diagonal element by that scalar.
| 4. What is an identity matrix and what are its properties? | |
Ans. An identity matrix is a square matrix with ones on the main diagonal and zeros elsewhere. The main diagonal elements are located from the top-left to the bottom-right of the matrix. The properties of an identity matrix include:
- Multiplying any matrix by an identity matrix results in the original matrix.
- The product of an identity matrix and any matrix is equal to the original matrix.
- The determinant of an identity matrix is always equal to 1.
| 5. What is a zero matrix and what are its properties? | |
Ans. A zero matrix is a matrix where all the elements are zero. It can be of any size, including square or rectangular matrices. The properties of a zero matrix include:
- Adding a zero matrix to any matrix does not change the original matrix.
- The product of any matrix and a zero matrix is always a zero matrix.
- The determinant of a zero matrix is always zero.
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