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Examples : Multiplication of a matrix by a scalar Video Lecture | Mathematics (Maths) Class 12 - JEE

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FAQs on Examples : Multiplication of a matrix by a scalar Video Lecture - Mathematics (Maths) Class 12 - JEE

1. What is matrix multiplication by a scalar?
Ans. Matrix multiplication by a scalar refers to the operation of multiplying every element of a matrix by a constant number, known as the scalar. Each element in the matrix is multiplied by the same scalar value.
2. How does matrix multiplication by a scalar affect the matrix?
Ans. When a matrix is multiplied by a scalar, each element in the matrix is multiplied by the scalar value, resulting in a new matrix with the same dimensions as the original. The scalar multiplication affects the magnitude of each element without changing the overall structure of the matrix.
3. What is the purpose of matrix multiplication by a scalar?
Ans. Matrix multiplication by a scalar is used in various mathematical and computational applications. It allows for scaling and rescaling of a matrix, which can be useful in operations such as adjusting the intensity of an image, scaling vectors, or representing transformations in linear algebra.
4. Can a matrix be multiplied by any scalar value?
Ans. Yes, a matrix can be multiplied by any scalar value, regardless of its magnitude or sign. The scalar can be positive, negative, or zero. Multiplying a matrix by a positive scalar will increase the magnitude of each element, while multiplying by a negative scalar will change the signs of the elements.
5. Does matrix multiplication by a scalar change the identity matrix?
Ans. No, matrix multiplication by a scalar does not change the identity matrix. The identity matrix is a special matrix that, when multiplied with any other matrix, results in the same matrix. Multiplying the identity matrix by a scalar only scales the elements of the identity matrix, but its structure remains unchanged.
204 videos|288 docs|139 tests

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