]Eigenvectors are found by the equation
implying that
. We then can write:
![A-\lambda I = \left [ \begin{array}{cc} 4-\lambda & 2 \\ 5 & 1-\lambda \end{array}\right ]](https://tex.z-dn.net/?f=%20A-%5Clambda%20I%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204-%5Clambda%20%26%202%20%5C%5C%205%20%26%201-%5Clambda%20%5Cend%7Barray%7D%5Cright%20%5D%20)
And:
Gives us the characteristic polynomial:
So, solving for each eigenvector subspace:
![\left [ \begin{array}{cc} 4 & 2 \\ 5 & 1 \end{array} \right ] \left [ \begin{array}{c} x \\ y \end{array} \right ] = \left [ \begin{array}{c} -x \\ -y \end{array} \right ]](https://tex.z-dn.net/?f=%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bcc%7D%204%20%26%202%20%5C%5C%205%20%26%201%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20x%20%5C%5C%20y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20%3D%20%5Cleft%20%5B%20%5Cbegin%7Barray%7D%7Bc%7D%20-x%20%5C%5C%20-y%20%5Cend%7Barray%7D%20%5Cright%20%5D%20)
Gives us the system of equations:
Producing the subspace along the line
We can see then that 3 is the answer.
Answer: Heater -Rs 2400; Fan- Rs 1600
Step-by-step explanation:
Given
Ajay bought a fan and a heater for Rs 4000
Suppose the price of fan is x and that of heater is 4000-x
Profit on the fan is 
Loss on heater is 
Total profit is 7% i.e. 
Thus, the price of heater is 
Price of fan is 
Price of heater is 
B.
7cd, -12cd
Explanation;
Like terms have similar variables.
The algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
The given statement is Cindy's age, x, is 3 times her age 6 years ago.
We need to represent the given statement as the algebraic expression.
<h3>What is an algebraic expression?</h3>
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations.
6 years ago Cindy's age(x) is x-6.
3 times Cindy's age=3(x-6)
Therefore, the algebraic expression for the statement Cindy's age, x, is 3 times her age 6 years ago is 3(x-6).
To learn more about the algebraic expression visit:
brainly.com/question/953809.
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