The matrix expressions are:
![\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}-15&-17\\26&29\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12%267%5C%5C5%263%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-15%26-17%5C%5C26%2629%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-1%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
- Matrix 2 cannot be solved
![\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}3&4\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%263%5C%5C-4%265%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%264%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%268%5Cend%7Barray%7D%5Cright%5D)
<h3>How to solve the matrix expression?</h3>
The rule for matrix product states that:
If the dimensions of matrix A is m by n, and the dimension of matrix B is n by p.
Then, the dimension of the product matrix is: m by p
Using the above rule, we have:
<u>Expression 1:</u>
![\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}a&b\\c&d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12%267%5C%5C5%263%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%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-1%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
Expand:
![\left[\begin{array}{cc}12a + 7c&12b + 7d\\5a + 3c &5b + 3d\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12a%20%2B%207c%2612b%20%2B%207d%5C%5C5a%20%2B%203c%20%265b%20%2B%203d%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-1%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
By comparison, we have:
12a + 7c = 2
5a + 3c = 3
12b+ 7d = -1
5b + 3d = 2
Using a graphing tool, we have:
a = -15, b = -17, c = 26 and d = 29
Hence, the matrix expression is:
![\left[\begin{array}{cc}12&7\\5&3\end{array}\right] * \left[\begin{array}{cc}-15&-17\\26&29\end{array}\right] = \left[\begin{array}{cc}2&-1\\3&2\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D12%267%5C%5C5%263%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-15%26-17%5C%5C26%2629%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D2%26-1%5C%5C3%262%5Cend%7Barray%7D%5Cright%5D)
<u>Expression 2:</u>
![\left[\begin{array}{cc}6.75&3\\-9&-4\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D6.75%263%5C%5C-9%26-4%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%26b%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%265%5Cend%7Barray%7D%5Cright%5D)
Expand:
![\left[\begin{array}{c}6.75a +3b\\-9a - 4b\end{array}\right] = \left[\begin{array}{c}8&5\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6.75a%20%2B3b%5C%5C-9a%20-%204b%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D8%265%5Cend%7Barray%7D%5Cright%5D)
By comparison, we have:
6.75a + 3b = 8
-9a - 4b = 5
Using a graphing tool, the system of equation has no solution
Hence, the matrix expression cannot be solved
<u>Expression 3:</u>
![\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}a&b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%263%5C%5C-4%265%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7Da%26b%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%268%5Cend%7Barray%7D%5Cright%5D)
Expand:
![\left[\begin{array}{c}-2a +3b &-4a +5b\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D-2a%20%2B3b%20%26-4a%20%2B5b%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%268%5Cend%7Barray%7D%5Cright%5D)
By comparison, we have:
-2a + 3b = 6
3a + 5b = 8
Using a graphing tool,
a = 3 and b = 4
Hence, the matrix expression is:
![\left[\begin{array}{cc}-2&3\\-4&5\end{array}\right] * \left[\begin{array}{c}3&4\end{array}\right] = \left[\begin{array}{c}6&8\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-2%263%5C%5C-4%265%5Cend%7Barray%7D%5Cright%5D%20%2A%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D3%264%5Cend%7Barray%7D%5Cright%5D%20%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bc%7D6%268%5Cend%7Barray%7D%5Cright%5D)
Read more about matrix at:
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Answer:
-9
Step-by-step explanation:
set y to 0
-2x + 1/2y = 18
-2x +1/2(0)=18
-2x / -2 = 18 /-2
x = -9
Answer:A
Step-by-step explanation:
f=(x)
Simplifying
120 + -28a = 78
Solving
120 + -28a = 78
Solving for variable 'a'.
Move all terms containing a to the left, all other terms to the right.
Add '-120' to each side of the equation.
120 + -120 + -28a = 78 + -120
Combine like terms: 120 + -120 = 0
0 + -28a = 78 + -120
-28a = 78 + -120
Combine like terms: 78 + -120 = -42
-28a = -42
Divide each side by '-28'.
a = 1.5
Simplifying
a = 1.5
Answer:A -3,6
Step-by-step explanation: Substitue the answers in and they work out