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
dusya [7]
2 years ago
9

Find the inverse of the matrix using elementary row operations on the augmented matrix

Mathematics
1 answer:
musickatia [10]2 years ago
5 0

The inverse of the matrix \vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right] is represented by the matrix \vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right].

<h3>How to determine the inverse matrix</h3>

A matrix <em>A</em> has an <em>inverse</em> matrix if and only if its determinant is different than 0. Given that we have a matrix formed by 2 rows and 2 columns, we can obtain the following <em>inverse</em> matrix by using the following formula:

\vec A ^{-1} = \frac{1}{\det (\vec A)} \cdot adj (\vec A)   (1)

Where adj (\vec A) is the adjoint of the matrix, which is the transposed of the <em>cofactor</em> matrix.

If we know that \vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right], then the inverse of the matrix is determined below:

\det (\vec A) = -2

adj (\vec A) = \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right]

\vec A^{-1} = -\frac{1}{2}\cdot \left[\begin{array}{cc}4&-2\\-3&1\end{array}\right]

\vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right]

The inverse of the matrix \vec A = \left[\begin{array}{cc}1&2\\3&4\end{array}\right] is represented by the matrix \vec A^{-1} = \left[\begin{array}{cc}-2&1\\\frac{3}{2} &-\frac{1}{2} \end{array}\right]. \blacksquare

To learn more on matrices, we kindly invite to check this verified question: brainly.com/question/11367104

You might be interested in
Which of the following is a solution of the inequality? -3 less than 2x+ 1 less than 5
Serhud [2]

Answer:

- 2 < x < 2

Step-by-step explanation:

Given

- 3 < 2x + 1 < 5 ( subtract 1 from each interval )

- 4 < 2x < 4 ( divide each interval by 2 )

- 2 < x < 2

7 0
4 years ago
Which two points are on the graph of g(x)=(1/5)^x
Orlov [11]
Sub. each value of x-coordinate into the function...
<span>If the y-coordinate is correct,Therefore,that is points on the graph.
 c is the correct ans .</span>
5 0
3 years ago
Galveston Island has a glass pyramid building with a rainforest ecosystem that tourists can visit while at the beach. The pyrami
Stolb23 [73]

100 feet. That's what I got.

5 0
3 years ago
Read 2 more answers
Solve the equation log^7b&gt;2
ahrayia [7]

Answer:

b > 12.71

Step-by-step explanation:

Here in this question we have to solve the inequality equation given for b (An unknown variable}

Now, the equation is (\log b)^{7} > 2

⇒ \log b > 2^{\frac{1}{7} }

We are taking the base of the log here is 10.

So, 10^{(\log b)} > 10^{2^{\frac{1}{7} } } {Since 10^{\log x} =x and e^{\ln x} = x}

⇒ b > 12.71 (Approximate) (Answer)

3 0
3 years ago
4x2 minus 20+48 factorise this polynomial completely
bulgar [2K]

Answer:

36

Step-by-step explanation:

With no parenthesis

7 0
3 years ago
Read 2 more answers
Other questions:
  • At Denver International Airport, 83% of recent flights have arrived on time. A sample of 12 flights is studied. (a) Calculate th
    14·1 answer
  • Zoo A has 109 monkeys while Zoo B has 67 monkeys. Which of the following is the best estimate of how many more monkeys Zoo A has
    14·2 answers
  • Alice kicks a 0.25 kg soccer ball with 0.5 N of force. What force does the ball exert on Alice’s foot as she kicks it?
    13·2 answers
  • Simplify: –3(y + 2)^2 – 5 + 6y
    11·2 answers
  • a ladder 5 meters long is leaning against a wall. the base of the ladder is sliding away from the wall at a rate of 1 meter per
    6·1 answer
  • Find the final price on a $1049 television that is on sale for 12% off if the sales tax is 4.5%
    5·1 answer
  • Which statements are true about points A, B, and C? Check all that apply.
    6·1 answer
  • Second question 200-200<br><br>how much I will give you branlys answer<br><br>good luck​
    13·2 answers
  • What is the value of x?<br> 68<br> 4x + 12<br> 17<br> 15<br> 32<br> 8
    10·1 answer
  • How many grams are equal to 8 kilograms?<br><br> Answer quick
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!