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
Ymorist [56]
3 years ago
14

Find the inverse of this matrix. 1 -1 -1 -1 2 3 1 1 4

Mathematics
1 answer:
zheka24 [161]3 years ago
3 0

Let's use Gaussian elimination. Consider the augmented matrix,

\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\-1 & 2 & 3 & 0 & 1 & 0\\1 & 1 & 4 & 0 & 0 & 1\end{array}\right]

• Add row 1 to row 2, and add -1 (row 1) to row 3:

\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 2 & 5 & -1 & 0 & 1\end{array}\right]

• Add -2 (row 2) to row 3:

\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 2 & 1 & 1 & 0\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]

• Add -2 (row 3) to row 2:

\left[\begin{array}{ccc|ccc}1 & -1 & -1 & 1 & 0 & 0\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]

• Add row 2 and row 3 to row 1:

\left[\begin{array}{ccc|ccc}1 & 0 & 0 & 5 & 3 & -1\\0 & 1 & 0 & 7 & 5 & -2\\0 & 0 & 1 & -3 & -2 & 1\end{array}\right]

So the inverse is

\begin{bmatrix}1&-1&-1\\-1&2&3\\1&1&4\end{bmatrix}^{-1} = \boxed{\begin{bmatrix}5&3&-1\\7&5&-2\\-3&-2&1\end{bmatrix}}

You might be interested in
the sum of 2 positive integers is 10. the difference of their reciprocals is 3/8. find both positive integers
Elena-2011 [213]

Answer:

The 2 integers would be: 2 and 8

Step-by-step explanation:

2 + 8 = 10

Reciprocal of 2: 1/2

Reciprocal of 8: 1/8

1 / 2 - 1 / 8 = 4/8 - 1/8 = <u>3/8</u>

4 0
2 years ago
Using Cramer's Rule, what are the values of x and y in the solutio
olya-2409 [2.1K]

Answer:

x = -3, y = 1

Step-by-step explanation:

To find the value of x and y, find the determinant of original matrix, which would be 21.

Then, substitute the value of x with the solutions to the equations and find the determinant of that matrix, which is -63.

Cramer's rule says that Dx ÷ D is the value of x. So, -63 ÷ 21 = -3.

So, the x-value is -3.

You can find the determinant of the y-value in the same way, and you'll find out that y = 1.

Hope this helped! :)

8 0
3 years ago
Pls Help im in a hurrry                                                                                                         
qwelly [4]

6  1/4 mark bainliest plzzz

5 0
3 years ago
Read 2 more answers
How many strings of eight uppercase English letters are there that start with X, if no letter can be repeated?
spin [16.1K]
X 25*24*23*22*21*20*19
which gives you
2,422,728,000
5 0
3 years ago
Trying to understand long division formula. 5 divided by 285.I have it down to 28-25 and i have 035 but why is 35 subtracted by
Sergeeva-Olga [200]

Explanation:

At each step, the product of the quotient digit and the divisor is subtracted from the dividend. This gives you the new dividend.

When the quotient digit is 7, the product of 7 and 5 is subtracted from the dividend. The dividend at that point is 35, so you have 35 - 35 = 0. The 0 is the next dividend. Among other things, that tells you you're done. (Any additional quotient digits will be zero.)

5 0
3 years ago
Other questions:
  • Solve |x| &gt; -9.<br><br> {x | x &lt; -9 or x &gt; 9}<br> all reals<br> no solution
    14·2 answers
  • For a craft project, two equilateral triangles are taped together to create a quadrilateral. What is the quadrilateral? rhombus
    12·2 answers
  • How to tell when to use positive or negative symbols when dividing?
    8·1 answer
  • Graph the solution set of x &lt; -8
    6·1 answer
  • Is y+3=x+6 a direct variation
    5·1 answer
  • Help! Brainliest to the first correct answer​
    5·1 answer
  • 16 7 9 2 6 8 16 11 x5 x8 x9 x 7 x 4 x 3 x 6 x 5. X4 0 2. 4 5 2. 5 33 15 7 x3 X1 x 7 x9 x 3 x22 x4 x6 x6 8 8 3 5 8 4. 4 x 7 X4 x3
    8·1 answer
  • When y is directly proportional to x, the value of y = -2 when x = 4. What is the value of y when x = 8?
    14·1 answer
  • A bicycle has a cash price of $319.95. It can be bought on hire purchase with a deposit of $69 and ten monthly installments of $
    5·1 answer
  • Parallelogram P Q S R is shown. The length of P Q is (2 x + 5) centimeters and the length of R S is (4 x + 1) centimeters.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!