Find DE if matrix D= Row 1= -2,4,6 and ROW 2= 5,-7,1 and matrix E= Row 1= 1,-2
Row 2= 0,-4, and Row 3= -3,4
WORK: [(-2)(1)+(4)(0)+(6)(-3)]=-20
[(-2)(-2)+(4)(4)+(6)(4)]=44
[(5)(1)+(-7)(0)+(1)(-3)]=2
[(5)(-2)+(-7)(4)+(1)(4)]=-34
The answers to choose from are:
A) Row 1= -20, 44 and Row 2= 8, -42
B) Row 1= -20, 8 and Row 2= 44, -42
I don't know where I am going wrong. Hopefully you can spot my error!!
Thanks.
I answered below. I agree with what you did to get
_-20___44
___2__-34
To find the product of two matrices D and E, we need to perform matrix multiplication. Given that matrix D has dimensions 2x3 (2 rows, 3 columns) and matrix E has dimensions 3x2 (3 rows, 2 columns), the resulting matrix will have dimensions 2x2.
To calculate the (1,1) entry of the resulting matrix DE, we need to take the dot product of the first row of D with the first column of E. Similarly, to calculate the (1,2) entry, we take the dot product of the first row of D with the second column of E. Following the same logic, we can calculate the entries (2,1) and (2,2) of the resulting matrix DE.
Let's perform the matrix multiplication step by step:
DE = [(-2)(1) + (4)(0) + (6)(-3)] [(-2)(-2) + (4)(4) + (6)(4)]
[(5)(1) + (-7)(0) + (1)(-3)] [(5)(-2) + (-7)(4) + (1)(4)]
Now, let's calculate the values:
DE = [-2 + 0 - 18] [-4 + 16 + 24]
[5 + 0 - 3] [-10 - 28 +4]
DE = [-20] [8]
[2] [-34]
Therefore, matrix DE is given by:
Row 1 = [-20, 8]
Row 2 = [2, -34]
Comparing this result with the given answer choices, we see that option B) matches the calculated result:
Row 1 = [-20, 8]
Row 2 = [2, -34]
Therefore, the correct answer is option B).