00:01
Here we determine the dimensions of matrix b such that the product of two matrices a b is given as this matrix and the dimensions of matrix a is given as 2 by 3.
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Let's see how to determine the dimensions of matrix b.
00:16
And for that we are going to understand the definition of a product of two matrices.
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That is, suppose if matrix a has dimensions m by n, that is it has m rows.
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The first number indicates the rows.
00:32
So it has m rows.
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And the second number indicates the column.
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So this one is n columns.
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And then the condition for matrix ab to be defined is such that the b matrix should have the dimensions of n rows and any number of columns.
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Let's say that it is p.
00:53
So this represents the rows for matrix p and this represents the column.
01:01
For the matrix b.
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And so that the product ab is defined, that is the product of two matrices, ab is defined.
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That is the number of columns in matrix a should match the number of rows in matrix b.
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Only then this product is defined.
01:21
And when we find the product, the dimension of this ab matrix will have m rows, whatever we have in the dimensions of matrix a, the number of rows, and then the number of columns, whatever we have for matrix b...