Could someone check this matrix calculation
The first matrix dimension is 1 by 3
row 1 = 1
row 2 = 7
row 3 =3
Second matrix is 1 by 3
Row 1 column one =2
row 1 column two = -5
row one column three = 5
my calculation is that it would be the dimensions of 3 by 3
Final calcs would be row 1 column 1 = 2
row one-column two = -1
row one column three = 5
row two column 1 = 14
row two column two= -7
row two column three = 35
row three column one = 6
row three column two = -3
row three column three = 15
Is that correct?
when you describe the first matrix as
row 1 = 1
row 2 = 7
row 3 =3
you are describing a column matrix with dimension 3 by 1 , not 1 by 3
so I see you multiplying
1
7
3
by
2 -5 5
I got
2 -5 5
14 -35 35
6 -15 15
I am used to this notation :
m by n matix has m rows and n columns
Are you not using that same notation?
anyway, you could not multiply a 1by3 by a 1by3, no matter what notation you are used to
To verify the matrix calculation, we need to perform matrix multiplication. Matrix multiplication is done by taking the dot product of each row of the first matrix with each column of the second matrix.
Given the first matrix A with dimensions 1 by 3 and the second matrix B with dimensions 1 by 3, we can calculate their multiplication as follows:
A = [1, 7, 3]
B = [2, -5, 5]
To calculate the value at the position (i, j) in the resulting matrix C, we need to perform the dot product of the ith row of A with the jth column of B. So,
C(1, 1) = A(1, 1) * B(1, 1) + A(1, 2) * B(2, 1) + A(1, 3) * B(3, 1)
= 1 * 2 + 7 * (-5) + 3 * 5
= 2 - 35 + 15
= -18
C(1, 2) = A(1, 1) * B(1, 2) + A(1, 2) * B(2, 2) + A(1, 3) * B(3, 2)
= 1 * (-5) + 7 * (-5) + 3 * (-5)
= -5 * (1 + 7 + 3)
= -5 * 11
= -55
C(1, 3) = A(1, 1) * B(1, 3) + A(1, 2) * B(2, 3) + A(1, 3) * B(3, 3)
= 1 * 5 + 7 * 5 + 3 * 5
= 5 * (1 + 7 + 3)
= 5 * 11
= 55
So, the resulting matrix C would have the dimensions 1 by 3 and its values would be:
C = [-18, -55, 55]
Comparing the calculated values with your results, it seems there was a mistake in the signs of some values.
Therefore, the correct matrix calculation would be:
row 1 column 1 = -18
row 1 column 2 = -55
row 1 column 3 = 55