Start by subtracting matrix D from matrix E. Then, multiply the obtained matrix by F.
34&-1 6&-13 -7&16
Practice makes perfect
We want to calculate the matrix product of (E-D)F if it is defined. Recall that we can multiply two matrices only if the number of columns of the first matrix is equal to the number of rows of the second matrix. Otherwise, the operation is undefined.
E D F
(
2 & -5 & 0 1 & 0 & -2 3 & 1 & 1
-
1 & 2 & - 1 0 & 3 & 1 2 & -1 & -2
)
*
-3 & 2 -5 & 1 2 & 4
3* 3 3* 3 3* 2
E-D
We first need to calculate E-D.
E D
([
cc
2 & -5 & 0 1 & 0 & -2 3 & 1 & 1
]
-
[
cc
1 & 2 & - 1 0 & 3 & 1 2 & -1 & -2
])
3* 3 3* 3
We can see that the given matrices have the same dimensions, 3* 3. Therefore, it is possible to perform the addition and subtraction of the given matrices. Let's do it!
Now, we can calculate (E-D)F. To do that, we will multiply the obtained matrix by F. The dimensions of matrix E-D are 3* 3, and the dimensions of F are 3* 2. This means that the number of columns of E-D is equal to the number of rows of F. Therefore, the multiplication is defined and the dimensions of the product will be 3 * 2.
[
ccc
1&-7&1 1&-3&-3 1&2&3
]
and
[
cc
-3 & 2 -5 & 1 2 & 4
]
cc
3* 3 & 3* 2
To multiply matrices, we use a process called the dot product. It follows a pattern of multiplying and adding terms across the rows of the first matrix and down the columns of the second one.
[
ccc
a & b & c
d & e & f
g & h & i
]
*
[
cc
j & k
l & m
n & o
]
=
[
cc
a j+ b l+ c n & ak+bm+co
dj+el+fn & dk+em+fo
gj+hl+in & gk+hm+io
]
Let's calculate it!
