Which of the following is correct about scalar multiplication of a matrix A?

Every element of a particular row is multiplied by the scalar when a matrix is multiplied by the scalar.

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Every element of the matrix is multiplied with the scalar when a matrix is multiplied with a scalar.

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One of the elements of the matrix is multiplied with the scalar when a matrix is multiplied with the scalar.

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Every element of a particular column is multiplied by the scalar when a matrix is multiplied by the scalar.

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Solution

The correct option is B
Every element of the matrix is multiplied with the scalar when a matrix is multiplied with a scalar.

We have discussed in the video that when a matrix, let’s say A is multiplied by a scalar k then to obtain k x A we have to multiply each element of matrix A by the scalar k and not a particular element or a particular row.

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Q. Assertion :If A is a square matrix of order n then

d e t (k A) = k^{n} | A |

Reason: If matrix B is obtained from A by multiplying any row (or column) by a non zero scalar k then

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Q. Which of the following algebraic operations with scalar and vector physical quantities are meaningful.

(i) adding any two vectors
(ii) adding a scalar to a vector of the same dimensions
(iii) multiplying any vector by any scalar
(iv) multiplying any two scalars
(v) adding any two scalars
(vi) adding a component of a vector to the same vector.

State with reasons, whether the following algebraic operations with scalar and vector physical quantities are meaningful:

(a) adding any two scalars, (b) adding a scalar to a vector of the same dimensions, (c) multiplying any vector by any scalar, (d) multiplying any two scalars, (e) adding any two vectors, (f) adding a component of a vector to the same vector.

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