Find –5A + 4B%0D%0A%0D%0AA equals%0D%0Astart 3 by 2 matrix%0D%0A1st row%0D%0A1st column 6%0D%0A2nd column 1%0D%0A2nd row%0D%0A1st column negative 4%0D%0A2nd column negative 6%0D%0A3rd row%0D%0A1st column 7%0D%0A2nd column negative 7%0D%0A%0D%0Aend matrix%0D%0A%0D%0AB equals%0D%0Astart 3 by 2 matrix%0D%0A1st row%0D%0A1st column negative 5%0D%0A2nd column negative 1%0D%0A2nd row%0D%0A1st column negative 3%0D%0A2nd column negative 8%0D%0A3rd row%0D%0A1st column 6%0D%0A2nd column 8%0D%0A%0D%0Aend matrix%0D%0A%0D%0A%0D%0A(1 point)%0D%0AResponses%0D%0A%0D%0A%0D%0AImage with alt text: matrix%0D%0A%0D%0A%0D%0AImage with alt text: matrix%0D%0A%0D%0A%0D%0AImage with alt text: matrix
To find -5A + 4B, we first need to compute the product of A and B.
Given A:
[6 1]
[-4 -6]
[7 -7]
And B:
[-5 -1]
[-3 -8]
[6 8]
We can perform matrix multiplication to find AB.
Product AB:
[(6*-5 + 1*-3) (6*-1 + 1*-8)]
[(-4*-5 + -6*-3) (-4*-1 + -6*-8)]
[(7*-5 + -7*6) (7*-1 + -7*8)]
Simplifying the products:
[-33 -14]
[18 -44]
[-17 49]
Now we can find -5A + 4B by multiplying each element of AB by -5 and each element of B by 4, and then subtracting.
-5A + 4B:
[(-33*-5 + -14*4) (-33*-1 + -14*8)]
[(18*-5 + -44*4) (18*-1 + -44*8)]
[(-17*-5 + 49*4) (-17*-1 + 49*8)]
Simplifying the products:
[115 -77]
[-86 -284]
[-83 298]
Therefore, -5A + 4B equals:
[115 -77]
[-86 -284]
[-83 298]
To find -5A + 4B, we need to multiply each element of matrix A by -5, and each element of matrix B by 4, and then subtract the corresponding elements.
A =
| 6 1 |
| -4 -6 |
| 7 -7 |
B =
| -5 -1 |
| -3 -8 |
| 6 8 |
-5A =
| -5*6 -5*1 |
| -5*(-4) -5*(-6) |
| -5*7 -5*(-7) |
-5A =
| -30 -5 |
| 20 30 |
| -35 35 |
4B =
| 4*(-5) 4*(-1) |
| 4*(-3) 4*(-8) |
| 4*6 4*8 |
4B =
| -20 -4 |
| -12 -32 |
| 24 32 |
Now, subtract the corresponding elements of -5A and 4B:
-5A + 4B =
| -30 -5 | + | -20 -4 |
| 20 30 | + | -12 -32 |
| -35 35 | + | 24 32 |
-5A + 4B =
| -30 - 20 -5 - 4 |
| 20 - 12 30 - 32 |
| -35 + 24 35 + 32 |
-5A + 4B =
| -50 -9 |
| 8 -2 |
| -11 67 |
Therefore, -5A + 4B is given by:
| -50 -9 |
| 8 -2 |
| -11 67 |
To find -5A + 4B, we first need to multiply the matrices A and B by their respective scalars and then subtract them.
Let's start with A:
A = [6 1]
[-4 -6]
[7 -7]
Now let's multiply each element of A by -5:
-5 * A = [-5*6 -5*1]
[-5*-4 -5*-6]
[-5*7 -5*-7]
Simplifying further:
-5 * A = [-30 -5]
[20 30]
[-35 35]
Next, let's work with matrix B:
B = [-5 -1]
[-3 -8]
[6 8]
Now let's multiply each element of B by 4:
4 * B = [4*-5 4*-1]
[4*-3 4*-8]
[4*6 4*8]
Simplifying further:
4 * B = [-20 -4]
[-12 -32]
[24 32]
Finally, let's subtract the two matrices:
-5A + 4B = [-30 -5] + [-20 -4]
[20 30] [-12 -32]
[-35 35] [24 32]
Combining the corresponding elements:
-5A + 4B = [-30-20 -5-4]
[20-12 30-32]
[-35+24 35+32]
Simplifying further:
-5A + 4B = [-50 -9]
[8 -2]
[-11 67]
So, -5A + 4B equals:
[-50 -9]
[8 -2]
[-11 67]