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No it can't !!!

Matrix property: A matrix A of dimension [nxm] can be multiplied by another B of dimension [ txs] <=> m=t.

m=t => there exist a C = A.B of dimension [nxs].

Observe that given [3x5] and [3x5], 5!=3(not equal to) so you can't!

Q: Can a 3 X 5 matrix be multiplied by a 3 X 5 matrix?

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No, but it can be multiplied: The new matrix is 3x3. EG: 100100 100 200 010010 x 010 = 020 001001 001 002 100 010 001

No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.

3 x 3 x 5 = 451 x 3 x 15 = 45

The first matrix has 3 rows and 2 columns, the second matrix has 2 rows and 3 columns. Two matrices can only be multiplied together if the number of columns in the first matrix is equal to the number of rows in the second matrix. In the example shown there are 3 rows in the first matrix and 3 columns in the second matrix. And also 2 columns in the first and 2 rows in the second. Multiplication of the two matrices is therefore possible.

3 multiplied by whatever the number that represents the variable x. Example: if x=5, then 3*5=15.

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Yes. If one matrix is p*q and another is r*s then they can be multiplied if and only if q = r and, in that case, the result is a p*s matrix.

No, but it can be multiplied: The new matrix is 3x3. EG: 100100 100 200 010010 x 010 = 020 001001 001 002 100 010 001

3 x 5^2 x 11 = 3 x 25 x 11 = 75 x 11 = 825

2 x 2 x 2 x 3 x 5 x 5 2 to the third, multiplied by 3, multiplied by 5 squared

That is called the identity matrix. For example, (3,1,4)t x (1,1,1) = (3,1,4)t In this case (1,1,1) is the identity matrix. Another example is 5 11 1 0 1 11 x = 4 3 0 1 4 3 (You will have to imagine the brackets around the matrices as I did not know how to draw them in.) In this case 1 0 is the identity matrix. 0 1

3 x 5 x 5 = 75

No. Matrix addition (or subtraction) is defined only for matrices of the same dimensions.

3 x 5 x 11

3 x 5 x 5

3 x 3 x 5 x 5 = 225

2 x 3 x 5

It will be a 2 x 5 matrix.