1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
boyakko [2]
3 years ago
8

Find c1 and c2 such that M2+c1M+c2I2=0, where I2 is the identity 2×2 matrix and 0 is the zero matrix of appropriate dimension.

Mathematics
1 answer:
Katyanochek1 [597]3 years ago
6 0

The question is missing parts. Here is the complete question.

Let M = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]. Find c_{1} and c_{2} such that M^{2}+c_{1}M+c_{2}I_{2}=0, where I_{2} is the identity 2x2 matrix and 0 is the zero matrix of appropriate dimension.

Answer: c_{1} = \frac{-16}{10}

             c_{2}=\frac{-214}{10}

Step-by-step explanation: Identity matrix is a sqaure matrix that has 1's along the main diagonal and 0 everywhere else. So, a 2x2 identity matrix is:

\left[\begin{array}{cc}1&0\\0&1\end{array}\right]

M^{2} = \left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right]

M^{2}=\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]

Solving equation:

\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+c_{1}\left[\begin{array}{cc}6&5\\-1&-4\end{array}\right] +c_{2}\left[\begin{array}{cc}1&0\\0&1\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]

Multiplying a matrix and a scalar results in all the terms of the matrix multiplied by the scalar. You can only add matrices of the same dimensions.

So, the equation is:

\left[\begin{array}{cc}31&10\\-2&15\end{array}\right]+\left[\begin{array}{cc}6c_{1}&5c_{1}\\-1c_{1}&-4c_{1}\end{array}\right] +\left[\begin{array}{cc}c_{2}&0\\0&c_{2}\end{array}\right] =\left[\begin{array}{cc}0&0\\0&0\end{array}\right]

And the system of equations is:

6c_{1}+c_{2} = -31\\-4c_{1}+c_{2} = -15

There are several methods to solve this system. One of them is to multiply the second equation to -1 and add both equations:

6c_{1}+c_{2} = -31\\(-1)*-4c_{1}+c_{2} = -15*(-1)

6c_{1}+c_{2} = -31\\4c_{1}-c_{2} = 15

10c_{1} = -16

c_{1} = \frac{-16}{10}

With c_{1}, substitute in one of the equations and find c_{2}:

6c_{1}+c_{2}=-31

c_{2}=-31-6(\frac{-16}{10} )

c_{2}=-31+(\frac{96}{10} )

c_{2}=\frac{-310+96}{10}

c_{2}=\frac{-214}{10}

<u>For the equation, </u>c_{1} = \frac{-16}{10}<u> and </u>c_{2}=\frac{-214}{10}<u />

You might be interested in
Select all the exspressions that are all equivalent to 20 percent of 150
Dmitriy789 [7]

<em>Note: It seems you may have unintentionally missed adding the answer choices. Thus, I am solving your question in general to give you the idea of how the percentage works, which anyways would solve your query.</em>

<em></em>

Answer:

Please check the explanation.

Step-by-step explanation:

Given that we have to determine the expressions which are equivalent to 20 percent of 150.

First, we need to determine what actually 20 percent of 150 really brings.

i.e

20% of 150 = 20/100 × 150

                   = 30

Thus,

20% of 150 = 30

Therefore, any expression that is equivalent to 30 will be included in the answer to this question.

4 0
3 years ago
Please help with question ​
leva [86]

Answer:

whats the question? whardo u have to find out

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Which property is this 16 + (c+ 17) = (16 + c) + 17
HACTEHA [7]
Associative property (associative laws)
8 0
3 years ago
Please help me ASAP!!!
OLga [1]

Answer: The answer would be B

Step-by-step explanation:

The reason for this is because the triangles are similar they are also congruent. df=bc, fe=ac, ed=ab.

Because de=ba and ba=4 in. that would mean that de would also be 4in.

3 0
3 years ago
PLEASE PLEASE HELP ME
Sidana [21]
Sum of angle in a triangle is 180, so 33+70+x=180
x=77
x and y are vertical angles so y=77
6 0
3 years ago
Read 2 more answers
Other questions:
  • Alaine has 1 gallon of paint. She is going to pour it into a paint tray that measures 10 inches wide, 12 inches long, and 5 cm d
    14·1 answer
  • MATH HELP PLEASE IT IS URGENT!!!! Worth 15 points, will even give 5 starts say thanks and give brainlest answer to the right ans
    15·1 answer
  • Which figure has the same area as the parallelogram shown below? A. A triangle with a base of 4 mm and a height of 20 mm B. A tr
    5·1 answer
  • Paul, Colin and Brian are waiters.
    11·1 answer
  • Which of the following is not a scatter plot below?
    15·1 answer
  • I WILL GIVE BRAINLIEST!! PLEASE HURRY
    8·1 answer
  • How many times bigger is a group of 21 marbles than a group of 7 marbles?
    13·1 answer
  • PLz help me i need to get 100
    5·2 answers
  • How to find an equation given the slope and y intercept.
    8·1 answer
  • Find the value of n in this equation.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!