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
Ierofanga [76]
3 years ago
10

Solve these linear equations by Cramer's Rules Xj=det Bj / det A:

Mathematics
1 answer:
timurjin [86]3 years ago
6 0

Answer:

(a)x_1=-2,x_2=1

(b)x_1=\frac{3}{4} ,x_2=-\frac{1}{2} ,x_3=\frac{1}{4}

Step-by-step explanation:

(a) For using Cramer's rule you need to find matrix A and the matrix B_j for each variable. The matrix A is formed with the coefficients of the variables in the system. The first step is to accommodate the equations, one under the other, to get A more easily.

2x_1+5x_2=1\\x_1+4x_2=2

\therefore A=\left[\begin{array}{cc}2&5\\1&4\end{array}\right]

To get B_1, replace in the matrix A the 1st column with the results of the equations:

B_1=\left[\begin{array}{cc}1&5\\2&4\end{array}\right]

To get B_2, replace in the matrix A the 2nd column with the results of the equations:

B_2=\left[\begin{array}{cc}2&1\\1&2\end{array}\right]

Apply the rule to solve x_1:

x_1=\frac{det\left(\begin{array}{cc}1&5\\2&4\end{array}\right)}{det\left(\begin{array}{cc}2&5\\1&4\end{array}\right)} =\frac{(1)(4)-(2)(5)}{(2)(4)-(1)(5)} =\frac{4-10}{8-5}=\frac{-6}{3}=-2\\x_1=-2

In the case of B2,  the determinant is going to be zero. Instead of using the rule, substitute the values ​​of the variable x_1 in one of the equations and solve for x_2:

2x_1+5x_2=1\\2(-2)+5x_2=1\\-4+5x_2=1\\5x_2=1+4\\ 5x_2=5\\x_2=1

(b) In this system, follow the same steps,ust remember B_3 is formed by replacing the 3rd column of A with the results of the equations:

2x_1+x_2 =1\\x_1+2x_2+x_3=0\\x_2+2x_3=0

\therefore A=\left[\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right]

B_1=\left[\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right]

B_2=\left[\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right]

B_3=\left[\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right]

x_1=\frac{det\left(\begin{array}{ccc}1&1&0\\0&2&1\\0&1&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{1(2)(2)+(0)(1)(0)+(0)(1)(1)-(1)(1)(1)-(0)(1)(2)-(0)(2)(0)}{(2)(2)(2)+(1)(1)(0)+(0)(1)(1)-(2)(1)(1)-(1)(1)(2)-(0)(2)(0)}\\ x_1=\frac{4+0+0-1-0-0}{8+0+0-2-2-0} =\frac{3}{4} \\x_1=\frac{3}{4}

x_2=\frac{det\left(\begin{array}{ccc}2&1&0\\1&0&1\\0&0&2\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)} =\frac{(2)(0)(2)+(1)(0)(0)+(0)(1)(1)-(2)(0)(1)-(1)(1)(2)-(0)(0)(0)}{4} \\x_2=\frac{0+0+0-0-2-0}{4}=\frac{-2}{4}=-\frac{1}{2}\\x_2=-\frac{1}{2}

x_3=\frac{det\left(\begin{array}{ccc}2&1&1\\1&2&0\\0&1&0\end{array}\right)}{det\left(\begin{array}{ccc}2&1&0\\1&2&1\\0&1&2\end{array}\right)}=\frac{(2)(2)(0)+(1)(1)(1)+(0)(1)(0)-(2)(1)(0)-(1)(1)(0)-(0)(2)(1)}{4} \\x_3=\frac{0+1+0-0-0-0}{4}=\frac{1}{4}\\x_3=\frac{1}{4}

You might be interested in
What is the length of a rectangle whose perimeter is 38 cm and its weight is 9 cm​
Tanzania [10]

Answer:

The length of the rectangle is 29 cm.

Step-by-step explanation:

38 - 9 = 29

8 0
3 years ago
Solve -8/5 x - 6 = -54
Musya8 [376]
The equation is false so no solution.

Simplify 8/5 * -6 to -48/5

Move the negative sign to the left

Simplify brackets

Since 48/5 = -54 its false so no answer
4 0
3 years ago
Read 2 more answers
Make r the subject of x= e + r/d
neonofarm [45]

Step-by-step explanation:

X=e+r/d

swap both sides

e+r/d=x

subtract e from both sides

e-e+r/d=x-e

r/d=x-e

multiply d to both sides

d×r/d=x-e×d

r=x-e×d

7 0
3 years ago
Solve for x<br> 7x + 8 = 29 (simplified please) ill give brainliest :)
mixer [17]

Answer: X=3

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
An amusement park reduced it's admission price to $15.50 per day, but now charges $1.50 per ride. Mark has $26 to spend on admis
gtnhenbr [62]
15.50+1.50x =26
1.50x = 10.50
x = 7
answer: he can ride 7 in one day
4 0
3 years ago
Other questions:
  • ​f(x)equals=18 x plus 1118x+11​, find ​f(44​).
    14·1 answer
  • What is the median value of the data set shown on the line plot?
    13·1 answer
  • Pls help 7th grade math your a life saver ❤
    8·2 answers
  • 2 Points<br> What is the slope of the line that contains the points (-2, 2) and (3,4)?
    11·1 answer
  • F(x) = log3(x + 4)<br> Find<br> f-1(2)
    14·1 answer
  • PLEASE HELP DUE IN 20 MINUTES
    5·1 answer
  • Please help me!!<br>basic Radicals <br>​
    8·1 answer
  • THE MEASURE OF TWO ADJACENT ANGLES OF THE PARALLELOGRAM ARE IN THE RATIO OF 3:2. FIND THE MEASURE OF EACH OF THE ANGLES OF THE P
    10·1 answer
  • Naomi is still not sure how many boxes of each type of candy to order. Her dad explains that he needs to do a little more mathem
    7·1 answer
  • *BRAINLIEST* (EASY QA: Warm UP) Find a positive solution to each equation: x2 = 1/4
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!