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
Triangle IJK, with vertices I(3,-8), J(9,-7), and K(5,-4), is drawn inside a rectangle, as shown below. What is the area, in squ
MA_775_DIABLO [31]

Answer:

11 sq units

Step-by-step explanation:

(6×4) - ½(6×1 + 4×3 + 2×4)

= 24 - ½(6+12+8)

= 24 - ½(26)

= 24-13

= 11 sq units

4 0
3 years ago
If there are 19 red marbles for every black marble in a bag of 120 marbles, how many red marbles are in the bag?
lesya692 [45]

Answer:6

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Kendra used these steps to solve the equation 2x + 5 = 3 + 2(x + 1). Which choice describes the meaning of her result, 5 = 5?
alekssr [168]
The answer is A.
 If a redundant conclusion is reached in basic algebra this states that the variable holds all possible real values. 
If you algebraically solve Kendra's you do achieve the true statement 5 = 5 (leaving out D). And if you test any value of x for the equation it does hold true (getting rid of B). 
Hopefully this makes sense.
6 0
3 years ago
Read 2 more answers
PLEASE HELP!!!!!!!! PLEASE DON’T SEND LINK(S). LOOK AT THE PICTURE HAS ALL THE INFORMATION.
Andreyy89

Answer:

The x-intercept is <u><em>5.</em></u>

Step-by-step explanation:

Hope this helped! :)

6 0
3 years ago
Read 2 more answers
Please help me w this an explain how you got it!.
pishuonlain [190]

Answer:

Vertex → (2, 4)

Step-by-step explanation:

Quadratic equation has been given as,

y = -x² + 4x

We rewrite this equation in the form of a function as,

f(x) = - x² + 4x

By comparing this equation with the standard quadratic equation,

y = ax² + bx + c

a = -1 and b = 4

Vertex of the parabola represented by this equation is given by [-\frac{b}{2a}, f(\frac{-b}{2a})]

x coordinate = -\frac{4}{2(-1)}

                     = 2

y-coordinate = f(2)

                     = - (2)² + 4(2)

                     = -4 + 8

                     = 4

Therefore, vertex of the given function is (2, 4)

6 0
2 years ago
Other questions:
  • Question
    11·1 answer
  • What’s the correct answer for this?
    12·2 answers
  • Solve for Z. 42=-7(z-3)
    14·2 answers
  • Write an equation of the line that passes through the point (3,0) and<br> has the slope, m = -2.
    10·1 answer
  • 30 points!!
    9·2 answers
  • Suppose you deposited ​$100 in a savings account 4 years ago. The simple interest rate is 2.9%. The interest that you earned in
    5·1 answer
  • What is the next fraction in this sequence? Simplify your answer.<br> 1 1 1 5<br> 6,4, 3, 12,
    10·1 answer
  • The baseball player threw the ball 30 feet to his teammate. How far would the throw be if measured in yards?
    14·1 answer
  • Write the slope-intercept form for the equation of the line through the given point with the given slope.
    7·1 answer
  • Fifteen hungry kittens found a bucket of sausages. Each time
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!