The adjoint of the matrix ![\left[\begin{array}{cc}1&0\\2&-1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D1%260%5C%5C2%26-1%5Cend%7Barray%7D%5Cright%5D)
is ![\left[\begin{array}{cc}-1&0\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
<h3>How to determine the adjoint?</h3>
The matrix is given as:
For a matrix A be represented as:
![A = \left[\begin{array}{cc}a&b\\c&d\end{array}\right]](https://tex.z-dn.net/?f=A%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Da%26b%5C%5Cc%26d%5Cend%7Barray%7D%5Cright%5D)
The adjoint is:
![Adj = \left[\begin{array}{cc}d&-b\\-c&a\end{array}\right]](https://tex.z-dn.net/?f=Adj%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7Dd%26-b%5C%5C-c%26a%5Cend%7Barray%7D%5Cright%5D)
Using the above format, we have:
![Adj = \left[\begin{array}{cc}-1&0\\-2&1\end{array}\right]](https://tex.z-dn.net/?f=Adj%20%3D%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bcc%7D-1%260%5C%5C-2%261%5Cend%7Barray%7D%5Cright%5D)
Hence, the adjoint of the matrix is
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If the first term is 5/3 and the common difference is 1/3. Then the infinite sum of the geometric series will be 2.5.
<h3>What is a series?</h3>
The sum of sequence terms is a series. That is, it is a list of integers connected by addition operations.
The sequence is given in the form of a variable.
The first term will be
And the common ratio will be
Then the sum of the geometric series will be given as
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Answer:
Step-by-step explanation:
(x + 5)2 + 2 = 42.5
x*2 + 5*2 + 2 = 42.5
2x + 10 + 2 = 42.5
2x + 12 = 42.5
2x = 42.5 - 12
2x = 30.5
x = 30.5/2
x = 15.25
Allow me to review before I start. Inconsistent means there's no solution to the system of simultaneous equations, i.e. parallel lines. Consistent means there's at least one solution. Independent and dependent apply to consistent systems. The former means exactly one solution (two lines in different directions which meet). Dependent means an infinite number of solution; the two lines are really the same line.
1. We have two different slopes, lines in two different directions, so they'll meet in exactly one place. That system is consistent and independent, the usual case.
2. We can write the first one y-3x= -2 and the second y-3x=+2. These are parallel lines that are different, so no solution: inconsistent.
3. The first equation is x+2y=4, same as the second. An infinite number of solutions. Consistent and dependent.
