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
Need help my answer is in blue
Bezzdna [24]
Yeah it's true, a point has no width, hight, or depth
4 0
3 years ago
Solve for x<br> 90°<br> \12x-22)<br> 170°
Y_Kistochka [10]

Answer:

x = 6

Step-by-step explanation:

Using this theorem to get the other angles of the triangle.

Angle at the vertex is equal to half of the angle at the intercepted arc

For the arc with angle 170degrees

Angle at the vertex = 1/2 * 170

Angle at the vertex = 85 degrees

For the arc with angle 90degrees

Angle at the vertex = 1/2 * 90

Angle at the vertex = 45 degrees

Taking the sum of the 3 angles and equating to 180

85 + 45 + 12x - 22 = 180

130-22+12x = 180

12x = 180 - 108

12x = 72

x = 72/12

x = 6

Hence the value of x is 6

5 0
3 years ago
Solve for y<br> 4y = 32<br> Please answer!
grigory [225]

Answer:

y = 8

Step-by-step explanation:

4t=32

Divide each side by 4

4y/4 = 32/4

y = 8

3 0
3 years ago
Read 2 more answers
Do You KNOW HOW?
ollegr [7]

Answer:

The type of association between x and y are inversely proportional  

Step-by-step explanation:

Solution:

Here the x value increase, the y value decrease which implies that x is inversely proportional to y

I hope this helps.

3 0
2 years ago
Read 2 more answers
X+2+y when x=1 And y=3
svet-max [94.6K]

Answer:

6

Step-by-step explanation:

1+2+3=6

5 0
3 years ago
Other questions:
  • Write in slope intercept form an equation of the line that passes through the given points
    5·1 answer
  • What number must you add to complete the square for x^2 + 4x = 15 ?
    8·1 answer
  • Please help me put these in the correct order. *No wrong answers* List the following in order Can you list the answers in order
    6·1 answer
  • Which of the following choices lists the values of the side longths of a triangle with 45-45-90 degree angles and a hypotonuso -
    7·2 answers
  • U = 4i + 9j<br> 8= -8j<br> Find: u +g
    6·1 answer
  • F(2)=-5x+6 find value
    14·1 answer
  • Solve for x <br><br><br><br><br><br>.problem down below ​
    15·1 answer
  • A
    12·1 answer
  • If ∠8 measures 116°, what is the measure of ∠1? (Lines b and c are parallel.)
    13·2 answers
  • 67 of the 645 parcels are damaged on the journey.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!