Answer:
![\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}3&1\\4&-2\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%5C%5C4%26-2%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3x%2B4y%26x-2y%5Cend%7Barray%7D%5Cright%5D)
Step-by-step explanation:
The general matrix representation for this transformation would be:
![\left[\begin{array}{cc}x&y\end{array}\right] * A = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5Cend%7Barray%7D%5Cright%5D%20%2A%20A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3x%2B4y%26x-2y%5Cend%7Barray%7D%5Cright%5D)
As the matrix A should have the same amount of rows as columns in the firs matrix and the same amount of columns as the result matrix it should be a 2x2 matrix.
![\left[\begin{array}{cc}x&y\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}3x+4y&x-2y\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dx%26y%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3x%2B4y%26x-2y%5Cend%7Barray%7D%5Cright%5D)
Solving the matrix product you have that the members of the result matrix are:
3x+4y = a*x + c*y
x - 2y = b*x + d*y
So the matrix A should be:
![\left[\begin{array}{cc}3&1\\4&-2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D3%261%5C%5C4%26-2%5Cend%7Barray%7D%5Cright%5D)
Answer:
Step-by-step explanation:
Let 
be the number of bags with 8 onions and let 
be the number of bags with 3 onions. We have the following system of equations:
Subtracting from both sides of the first equation, we get 
. Substitute this into the second equation:
Therefore, the number of 8-onion bags is:
Thus, the chef got 4 8-onion bags and 3 3-onion bags.
Answer: The answer is -0.5<-0.25
Step-by-step explanation:
Answer:
$916.67
Step-by-step explanation:
The remaining amount is 2/3 of the total. 3/4 of that is ...
(2/3)(3/4) = 2/4 = 1/2
of the total amount. Altogether, Carmen will have saved ...
1/3 + 1/2 = (2/6) +(3/6) = 5/6
of the total amount by the end of the year. She will have saved ...
$1100 × 5/6 ≈ $916.67 . . . . year-end total savings
Answer:
= 486 in²
Step-by-step explanation:
Linear scale factor = Image distance/object distance
Therefore; Linear scale factor = OL'/OL
= 54/ 12
= 9/2
Area scale factor is equivalent to the square of linear scale factor
Thus;
Area scale factor = (9/2)²
= 81/4
Hence; 81/4 = Area of larger rectangle/Area of smaller rectangle
Area of the smaller rectangle = 4 ×6 = 24 in²
Therefore;
Area of enlarged or larger pic = 81/4× 24
<u>= 486 in²</u>
