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Identity Matrix Video Lecture | Mathematics (Maths) Class 12 - JEE

204 videos|288 docs|139 tests

Timeline

00:03 Introduction
00:10 What is Multiplicative Identity?
00:48 Identity Matrix
01:22 Unit Matrix
02:10 How to find Identity Matrix?
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FAQs on Identity Matrix Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is an identity matrix?
Ans. An identity matrix is a square matrix in which all the elements in the main diagonal are ones, while all the other elements are zeros. It is denoted by the symbol "I" or "I_n", where "n" represents the size of the matrix.
2. What are the properties of an identity matrix?
Ans. The properties of an identity matrix include: - The product of any matrix and its corresponding identity matrix is equal to the original matrix. - The product of an identity matrix and any matrix is equal to the original matrix. - The identity matrix is commutative under matrix multiplication.
3. How can we determine whether a matrix is an identity matrix or not?
Ans. To determine whether a matrix is an identity matrix, we need to check the following conditions: - The matrix must be square, i.e., it should have an equal number of rows and columns. - All the elements in the main diagonal should be ones. - All the elements outside the main diagonal should be zeros.
4. What is the significance of an identity matrix in matrix operations?
Ans. The identity matrix serves as the equivalent of the number "1" in matrix operations. When a matrix is multiplied by the identity matrix, it remains unchanged. It acts as a neutral element, similar to how multiplying a number by 1 does not change its value. The identity matrix plays a crucial role in solving systems of linear equations, matrix inverses, and other matrix operations.
5. Can an identity matrix have a size other than a square matrix?
Ans. No, an identity matrix is always a square matrix. This means that it has an equal number of rows and columns. Each square matrix has a unique identity matrix associated with it, and its size is determined by the number of rows (or columns) it has.
204 videos|288 docs|139 tests

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