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Finding Inverse of Matrix using Elementary Operations Video Lecture | Mathematics (Maths) Class 12 - JEE
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FAQs on Finding Inverse of Matrix using Elementary Operations Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. How do elementary operations help in finding the inverse of a matrix? |  |
| 2. What are the elementary row operations used in finding the inverse of a matrix? | |
Ans. The elementary row operations used in finding the inverse of a matrix are:
1) Swapping two rows
2) Multiplying a row by a non-zero scalar
3) Adding a multiple of one row to another row
| 3. Can any matrix have an inverse? | |
Ans. No, not all matrices have an inverse. A matrix is said to be invertible or nonsingular if its determinant is non-zero. Only invertible matrices can have an inverse. If a matrix is singular, meaning its determinant is zero, it does not have an inverse.
| 4. What is the significance of the inverse of a matrix? | |
Ans. The inverse of a matrix is significant because it allows us to solve systems of linear equations, calculate the inverse of linear transformations, and perform various other mathematical operations. It acts as a counterpart to division in ordinary arithmetic.
| 5. Is it possible for a matrix to have more than one inverse? | |
Ans. No, a matrix cannot have more than one inverse. If a matrix has an inverse, it is unique. If we assume that a matrix has two inverses, A and B, then AB = I (where I is the identity matrix) and BA = I. By multiplying both equations, we get ABA = I, which implies that A = B. Therefore, the inverse of a matrix is always unique.
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