Overview
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Matrix Addition and Subtraction
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Matrix Multiplication
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Matrix Transformations
Matrix Addition and Subtraction
How to add matrices together:
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In order to add matrices together they must have the same dimensions
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For example:
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There is no solution as the two matrices have different dimensions
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However, when they have a same dimensions addition and subtraction is possible
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In order to add matrices we just add the numbers in each position together
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For example:
Practice Question:
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Solutions :
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Matrix Multiplication
How to know if matrix multiplication is possible:
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We need to look at the dimensions of both matrices
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If the number of columns on one matrix is equal to the rows of the other then multiplication is possible:
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Here our first matrix is a 2x2 and the second matrix is a 2x1
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As the number of columns on the first matrix is 2 and the number of rows on the second matrix is 2, then multiplication is possible
How to find what the dimensions the new matrix is:
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To find out the dimensions of the new matrix we need to look at the rows of the first matrix and the columns of the second:
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Here the first matrix has 2 rows and the second matrix has 1 column
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Therefore the matrix formed is a 2x1 matrix
How to multiply matrices:
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Once we know the dimensions of the new matrix we have consider each number in the matrix
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For example:
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For a we need to multiply the top row of the first matrix by the column in the second matrix
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For be we need to do the same but with the bottom row of the first matrix
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Therefore the answer is
Practice Questions:
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Solutions:
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Matrix Transformations
The identity matrix:
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Multiplying by it has no effect
Different Types of transformation matrices:
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Rotation 90 degrees anticlockwise around origin:
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Rotation 180 degrees anticlockwise around origin:
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Rotation 270 degrees anticlockwise around origin:
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Reflections in line x = 0:
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Reflection in line y = 0:
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Reflection in line y = x:
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Reflection in line y = -x:
Combining Matrices:
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If a point is transformed by matrix A followed by matrix B, we are able to combine these transformations to be represented by 1 matrix
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This matrix is equal to BA
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For example:
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Here we must do B x A in order to find C
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Hence this is the answer
Practice Question:
Solution:
