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
ch4aika [34]
3 years ago
11

FURTHER MATHEMATICS Use determinants to solve the systems of equation:

Mathematics
1 answer:
maw [93]3 years ago
8 0

Answer:

Step-by-step explanation:

\left\{\begin{array}{ccc}2x+1y+2z&=&13\\1x+1y-2z&=&8\\1x+2y+1z&=&11\\\end{array}\right.\\\\\\\Delta=\left| \begin{array}{ccc}2&1&2\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\1&1&-2\\1&2&1\end{array}\right| =2*\left| \begin{array}{ccc}1&\frac{1}{2}&1\\0&\frac{1}{2}&-3\\0&1&3\end{array}\right| =2*(\frac{3}{2}+3)=9\\\\

\Delta_1=\left| \begin{array}{ccc}13&1&2\\8&1&-2\\11&2&1\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\8&1&-2\\\frac{11}{2}& 1&\frac{1}{2}\end{array}\right| =2*\left| \begin{array}{ccc}13&1&2\\-5&0&-4\\\frac{-5}{2}& 0&\frac{5}{2}\end{array}\right| \\\\=2*(-1)*(\frac{-25}{2}-\frac{20}{2}) =45\\

\Delta_2=\left| \begin{array}{ccc}2&13&2\\1&8&-2\\1&11&1\end{array}\right| \\\\\\=\left| \begin{array}{ccc}3&21&0\\3&30&0\\1&11&1\end{array}\right| \\\\\\=1*(90-63) =27\\

\Delta_3=\left| \begin{array}{ccc}2&1&13\\1&1&8\\1&2&11\end{array}\right| \\\\\\=\left| \begin{array}{ccc}0&-1&-3\\0&-1&-3\\1&2&11\end{array}\right| \\\\\\=0\\

\left\{\begin{array}{ccc}x=\dfrac{\Delta_1}{\Delta}=\dfrac{45}{9}=5\\\\y=\dfrac{\Delta_2}{\Delta}=\dfrac{27}{9}=3\\\\z=\dfrac{\Delta_3}{\Delta}=\dfrac{0}{9}=0\\\end{array}\right.

You might be interested in
D=150 ft r=20 ft per min. t=?
Rama09 [41]
T=d/r 
plug in your numbers and divide then you have your answer. 
7 0
4 years ago
Please help ASAP.......
marta [7]

Answer:

The answer is x=10

Step-by-step explanation:

5/6x - 10 = 1/3x -5 multiple both sides by 6

5x - 60 = 2x -30 move the terms

5x - 2x = -30 +60

3x = 30 divide by 3

x = 10

3 0
3 years ago
Work out the percentage change to 2 decimal places when a price of £125.99 is increased to £150.
gizmo_the_mogwai [7]

Answer:

Percent change is 19.06%

Step-by-step explanation:

It is given that:

Price before change = £125.99

Price after increase = £150

Change = 150 - 125.99 = £24.01

Percent of change = \frac{Change}{Price\ before\ change}*100

Percent of change = \frac{24.01}{125.99} * 100

Percent of change = 0.1906 * 100

Percent of change = 19.06%

Therefore,

Percent change is 19.06%

4 0
3 years ago
Which equations are correct?
stepan [7]

Answer:

3y^5(2y^3+3)=−6y^8−9y^5

−2c^6(5c^3+6)=−10c^9−12c^6

are the correct equations.

Step-by-step explanation:

If you simply all these equations you will get following equations :

when bases are same and are in multiplication we add the exponents.

−4b^4(5b^2+6)=−20b^6−24b^4

−5x^3(3x^3+2)=−15x^6−10x^3

−3y^5(2y^3+3)=−6y^8−9y^5

−2c^6(5c^3+6)=−10c^9−12c^6

so equation 3 and 4 are correct.

5 0
3 years ago
Students at a local school can join one club. The chart below shows how many students are in each club. What percentage of the t
ss7ja [257]

Answer:

boto

Step-by-step explanation:

pink dolphin

8 0
3 years ago
Other questions:
  • Convert the repeating decimal 0.2323232323...... into a fraction.
    13·1 answer
  • I need help with this
    10·2 answers
  • The table represents a function what is the value of f(-1)?
    8·1 answer
  • Find the missing triangle. Leave answer in simplest radical form. Also please explain clearly.
    6·1 answer
  • Which set of numbers can represent the lengths of the sides of a right triangle? Round to the nearest whole number.
    7·1 answer
  • 21x21=x<br><br> What is x equal?
    7·2 answers
  • Calculate the mean and median ages. a. The mean age is 38.28. The median age is 38. b. The mean age is 38. The median age is 38.
    6·1 answer
  • What is 24/30 simplified
    15·2 answers
  • Simplify 6⁢(3⁢x - 5) + 5⁢(2⁢x - 1).
    11·1 answer
  • Can someone help me with this please
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!