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
What are 2 ways to solve the problem 9×1×5 = ?
aliina [53]
2ways you can solve that is by multiplying 9 by 1 then by 5 or 9by 5 then by 1
6 0
3 years ago
Which points of the following points are solutions to the equation 3x-4y-8=12
Natali [406]

Answer:

(0, -5), (4, -2), (-16, -17)

Step-by-step explanation:

I attach your full question in the image below

The equation is

3x-4y-8=12

Which can be rewritten as

3x-4y =12 +8

3x-20 = 4y

y = (3/4)*x - 5

We need to check each individual case

(0,-5)

y = (3/4)*(0) - 5  

y = -5

True

(4,-2)

y = (3/4)*(4) - 5  

y = -2

True

(8,2)

y = (3/4)*(8) - 5  

y = 1

False

(-16,-17)

y = (3/4)*(-16) - 5  

y = -17

True

(-1,-8)

y = (3/4)*(-1) - 5  

y = -23/4

False

(-40,-34)

y = (3/4)*(-40) - 5  

y = -35

False

(0,-5) (4,-2) and (-16,-17) are the solutions

8 0
3 years ago
PLEASE ANSWER + BRAINLIEST!!!!
Nookie1986 [14]
Plug in 6 for x and solve out for f(x)
8 0
3 years ago
What division sentence means the same as the following subtraction sentences?​
WINSTONCH [101]

I do not see any illustrations, but repeated subtraction is the exact same as division.

I hope this answer was useful, and as always, I am joyous to assist anyone at any time.

3 0
3 years ago
What is the value of <img src="https://tex.z-dn.net/?f=%20a_%7B1%7D%20" id="TexFormula1" title=" a_{1} " alt=" a_{1} " align="ab
julia-pushkina [17]
The correct awnser is a or c i hope i helped
8 0
3 years ago
Other questions:
  • Using a picture, show house six people could share for sandwiches. Then, write an equation and solve.
    9·1 answer
  • Divers looking for a sunken ship have defined the search area as a triangle with adjacent sides of length 2.75 miles and 1.32 mi
    12·1 answer
  • Can someone help? What is the answer to this? I need it by 4pm (10^2 - 4 x 8) divided by (8+ 9) The '^' stands for 'to the power
    7·1 answer
  • Help out please and please write answer in a decimal
    10·2 answers
  • Please help! I will give brainliest!
    15·1 answer
  • What is 12375/4 simplified
    13·1 answer
  • What is 0.818181818181818181 as a fraction
    13·1 answer
  • 2/5 / 2/3 how to divide fractions?
    12·1 answer
  • Answer please helpppp!!!
    5·2 answers
  • Write an equation that expresses the following relationship.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!