00:01
Hello, let's have a look at the question.
00:02
So the question state that suppose a is a 2 by 2 matrix.
00:07
So we have a is a 2 by 2 matrix and b is a 3 by 3 matrix and then we have c which is a 2 by 3 matrix and d which is a 3 by 2 matrix.
00:24
Now here it is given can the following product matrix be calculated? specify yes or no and do not calculate the product matrix.
00:34
So first of all before beginning the question we know that two matrices let us assume we have x and y are said to be conformable for the product if we have that the number of columns of x is equals to the number of rows of y.
01:19
Let us say that x has the matrix as a by b and y has the matrix as c by d.
01:31
So here this b should be equals to this c.
01:36
Now let us take the first part that is a.
01:41
Here we have said that we have ab.
01:44
Now we know that a has the matrix 2 by 2 and b has the matrix 3 by 3.
01:55
So here we see that these two are not equal.
01:59
That is the number of columns in a is not equals to the number of rows in b.
02:04
So therefore we say that the no the product can't be calculated.
02:08
Next b part we have ac.
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So we have a a 2 by 2 matrix and c we have a 2 by 3 matrix.
02:20
So here we see that these two are equal.
02:23
Therefore yes the product can be calculated.
02:26
Next in the c part we have ad.
02:30
So again a is 2 by 2 matrix and d is 3 by 2 matrix.
02:36
So again here we have 2 and 3 which are not equal.
02:40
So the answer is no the product can't be calculated.
02:43
Then d part we have bc.
02:47
So b has the matrix as 3 by 3 and c has the matrix as 2 by 3.
02:54
So again here we have 3.
02:57
It does not equals to 2.
02:59
So the answer is no.
03:00
Then in the e part we have bd.
03:05
B is a 3 by 3 matrix and d is a 3 by 2 matrix.
03:12
So here we see that 3 is equals to 3.
03:15
So the answer is yes...