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
3241004551 [841]
3 years ago
10

Find the inverse of the given​ matrix, if it exists.Aequals=left bracket Start 3 By 3 Matrix 1st Row 1st Column 1 2nd Column 0 3

rd Column negative 2 2nd Row 1st Column 4 2nd Column 1 3rd Column 3 3rd Row 1st Column negative 4 2nd Column 2 3rd Column 3 EndMatrix right bracket 1 0 −2 4 1 3 −4 2 3
Mathematics
1 answer:
BabaBlast [244]3 years ago
6 0

Answer:

A^{-1}=\left[ \begin{array}{ccc} \frac{1}{9} & \frac{4}{27} & - \frac{2}{27} \\\\ \frac{8}{9} & \frac{5}{27} & \frac{11}{27} \\\\ - \frac{4}{9} & \frac{2}{27} & - \frac{1}{27} \end{array} \right]

Step-by-step explanation:

We want to find the inverse of A=\left[ \begin{array}{ccc} 1 & 0 & -2 \\\\ 4 & 1 & 3 \\\\ -4 & 2 & 3 \end{array} \right]

To find the inverse matrix, augment it with the identity matrix and perform row operations trying to make the identity matrix to the left. Then to the right will be inverse matrix.

So, augment the matrix with identity matrix:

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

  • Subtract row 1 multiplied by 4 from row 2

\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ -4&2&3&0&0&1\end{array}\right]

  • Add row 1 multiplied by 4 to row 3

\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&2&-5&4&0&1\end{array}\right]

  • Subtract row 2 multiplied by 2 from row 3

\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&-27&12&-2&1\end{array}\right]

  • Divide row 3 by −27

\left[ \begin{array}{ccc|ccc}1&0&-2&1&0&0 \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]

  • Add row 3 multiplied by 2 to row 1

\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&11&-4&1&0 \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]

  • Subtract row 3 multiplied by 11 from row 2

\left[ \begin{array}{ccc|ccc}1&0&0&\frac{1}{9}&\frac{4}{27}&- \frac{2}{27} \\\\ 0&1&0&\frac{8}{9}&\frac{5}{27}&\frac{11}{27} \\\\ 0&0&1&- \frac{4}{9}&\frac{2}{27}&- \frac{1}{27}\end{array}\right]

As can be seen, we have obtained the identity matrix to the left. So, we are done.

You might be interested in
SOMONE HELP ME I HAVE <br> TO DO THIS AFTER SCHOOL PLS ASAP!!!
Scrat [10]

Answer:

1 no

2 I don't know

3 no

4 yes

5 2.5 is the slope

6 -0.5

7 no slope

Step-by-step explanation:

1 no because the y overlaps

2 not sure

3 it over laps

4 it never overlaps

5 y=2.5x-3

6 y=-0.5x+1

7 no slope it's just x=-2

for the 5-7 you can type that into demos and get more info

y=mx+b

m is the slope and b is y intercept

3 0
2 years ago
A store prices tapes by raising the wholesale price 50% and adding 25 cents .What must a tape's wholesale price be if the tape s
Andre45 [30]

Let's call the store value as s and the wholesale price as w. A store prices tapes by raising the wholesale price 50%(0.5 in decimals) and adding 25 cents, writing this as an equation, we have

s(w)=w+0.5w+0.25

If we invert the equation we're going to find the the wholesale price as a function of the store price.

\begin{gathered} s=w+0.5w+0.25 \\ s=1.5w+0.25 \\ s-0.25=1.5w \\ w(s)=\frac{s-0.25}{1.5} \end{gathered}

Now, to find the wholesale price if the sales price is $1.99, we just need to evaluate s = 1.99 on the function we created.

w(1.99)=\frac{1.99-0.25}{1.5}=1.16

The wholesale price is $1.16.

5 0
1 year ago
HELP WITH DIS GEOMETRY QUESTION!!!!!!!
Rus_ich [418]
To find the volume<span>, we use the formula V = (1/3)AH, where A = area of the </span>pyramid's base and H = height of the pyramid<span>.

Hope this helped</span>
8 0
3 years ago
Read 2 more answers
Question: "If y &gt; 3, what is the value of n ?"
iris [78.8K]

Answer:

y-3

Problem:

What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?

Step-by-step explanation:

Dividend=quotient×divisor+remainder

So we have

xy-3=(x-1)×(y)+remainder

xy-3=(xy-y)+remainder *distributive property

Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.

We need to get rid of minus y so we need plus y in the remainder.

We also need minus 3 in the remainder.

So the remainder is y-3.

Let's try it out:

xy-3=(xy-y)+remainder

xy-3=(xy-y)+(y-3)

xy-3=xy-3 is what we wanted so we are done here.

7 0
2 years ago
Find an equation in slope-intercept form for the line with slope -3/4 and y-intercept=0? will give BRAINLIEST
nata0808 [166]

Answer:

Step-by-step explanation:

See the solution process below:

Explanation:

The slope-intercept form of a linear equation is:  y =mx+b

Where  m is the slope and b

is the y-intercept value.

We are given the slope in the problem so we can substitute

−5/6 for  m  in the formula.

And,

(0,6)

is the y-intercept so we can substitute

6

for

b

in the formula giving:

y

=

−

5

6

x

+

6

6 0
3 years ago
Read 2 more answers
Other questions:
  • A chemistry teacher needs to mix a 40%
    15·1 answer
  • ASAP WILL MARK BRAINLYEST TO FIRST PERSON WHO ANSWERS!!!
    15·1 answer
  • How to solve this equation by using elimination?
    13·1 answer
  • What is the product of (2p + 7)(3p2 + 4p – 3)?
    11·2 answers
  • I WILL MARK BRAINLIEST TO WHOEVER GETS IT FIRST.
    14·2 answers
  • Between what two integers on a number line would \sqrt[3]{35}35 3 be plotted?
    7·2 answers
  • 3. Find the slope and y-intercept of the graph of the following equation.<br> 2y + 4 = -6x
    12·1 answer
  • Solve for x: 3x - 5 = -2x + 40
    13·1 answer
  • Which statement accurately describes the number and type of solutions for this quadratic, x^(2)-5x+1=0
    12·1 answer
  • Write the inequality:<br><br> Two less than twice a number is less than a half.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!