Introduction:

Multiplying an integer by a 2x2 matrix is a common operation in linear algebra and computer graphics. This operation involves scaling each element of the matrix by the integer.



Understanding the Multiplication Process:



The process entails taking a scalar (an integer) and multiplying it with each element of a 2x2 matrix.

The result is a new matrix where every element has been scaled by the scalar value.

Procedure for Multiplication:



For a 2x2 matrix represented as:

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[ a, b ]

[ c, d ]

and a scalar integer value, say x:

Multiply each element of the matrix by x:

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[ x*a, x*b ]

[ x*c, x*d ]

Example:



If you multiply the integer 3 by the 2x2 matrix:

[ 2, 4 ]

[ 1, 5 ]

The resulting matrix is:

[ 3*2, 3*4 ]

[ 3*1, 3*5 ]

Which simplifies to:

[ 6, 12 ]

[ 3, 15 ]

Key Points to Remember:



This operation is a fundamental aspect of matrix algebra.

It's used to scale or transform matrices, which has applications in various mathematical and practical fields.

Practical Applications:



Multiplying integers by matrices is particularly important in transforming geometric objects, scaling in computer graphics, and in various linear algebra applications.