Solve the system of linear equations using matrices.
2x+y+z=3
-x+y-6z=-24
x+6y+6z=-4

The solution is ____ ​(Type an exact answer in simplified​ form.)

Answers

Answer 1

Answer:

  (x, y, z) = (2, -4, 3)

Step-by-step explanation:

It is convenient to let an appropriate calculator reduce the augmented matrix to reduced row-echelon form. The rightmost column in that form is the solution vector [x, y, z].

__

If you want to solve this by hand, you can perform the following row operations to reduce the augmented matrix as shown in the attachment.

r1 ← r2 +r3; r2 ← (r2 +r3)/7 . . . . use this matrix for the next row replacement

r3 ← (r3 -r1 -4·r2)/11 . . . . . . . . . . use this matrix for the next row replacement

r1 ← r1 -2·r2 +5·r3

__

r1, r2, r3 refer to rows 1, 2, 3, respectively. The indicated multiplication and division are scalar operations, operating on each individual term in the row.

_____

Additional comment

Most graphing calculators have matrix solving functions. Apps are available for phone and tablet that will do this, and there are online websites that will reduce an augmented matrix as well.

Solve The System Of Linear Equations Using Matrices.2x+y+z=3-x+y-6z=-24x+6y+6z=-4The Solution Is ____

Related Questions

End is making some pancakes for himself and five friends. The ingredients he needs are shown in the list below.

Pancakes (serves 2)
2/3 milk
3/4 flour
3/2 sugar
1 Egg

a. How many cups of flour will Ed need?
b. How many teaspoons of sugar will Ed need?​

Answers

Answer:

a. 2 1/4 cup of flour

b. 4 1/2 tsp. off sugar

Step-by-step explanation:

Since the recipe serves 2, the answer given will feed 5 (6) people.

PLS DO THE MATH INT HE PICTURE

Answers

Answer:

Area = 100cm²

Perimeter = 48cm

The function f(x) = -2x^5 + x^3 - 7x is an odd function. Which rule is satisfied by this function?
A. f(x) = f(-x)
B. f(x) = -f(x)
C. -f(x) = f(-x)
D. f(x) = f(x)^-1

Answers

[tex]f(x) = -2x^5 +x^3 -7x \\\\-f(x) =-(-2x^5 +x^3 -7x) = 2x^5 -x^3 +7x = x(2x^4 - x^2 +7)\\\\f(-x) = -2(-x)^5 + (-x)^3 -7(-x) = 2x^5 -x^3 +7x = x(2x^4 -x^2 +7) \\\\\\\text{Hence,} ~ -f(x)=f(-x)[/tex]

In △ABC, m∠A = 75° and m∠C = 20°, What is m⁢∠⁡⁣B?

Answers

Answer:

30 degree ok please make me brainliest

Answer:

∠ B = 85°

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180° , that is

∠ A + ∠ B + ∠ C = 180° , substitute values

75° + ∠ B + 20° = 180°

∠ B + 95° = 180° ( subtract 95° from both sides )

∠ B = 85°

Calculator
Which ordered pair is the solution to the system of equations?
1 -5x - 3y = 12
Y=x-12
0 (0, -4)
0 (-6, 6)
O (1, -11)
O (3,-9)

Answers

[tex] \text{Given : Which ordered pair is the solution to the system of equations?} \\ \\ \begin{cases}-5x - 3y = 12 \\ y - x = 12 \end{cases} [/tex]

[tex] \text{Solution : According to the question, here let's take these variables as two} \\ \text{equations then get their value and finally get the answer.} \\ \\ \sf {1}^{st} \: equation : \\ \leadsto \frak{-5x - 3y = 12} \\ \\ \leadsto \frak{-5x = 12 + 3y} \\ \\ \leadsto \frak{x= \frac{12 + 3y}{-5}} \qquad \sf ...eq(1) \\ \\ \sf 2^{nd} \: equation : \\ \leadsto \frak{y = x - 12} \qquad \sf ...eq(2) \\ \\ \underline{ \frak{finding \: x }} : \\ \\ \dashrightarrow \frak{x= \frac{12 + 3y}{-5}} \\ \\ \dashrightarrow \frak{x= \frac{12 + 3(x - 12)}{-5}} \\ \\ \dashrightarrow \frak{x= \frac{12 + 3x - 36}{-5}} \\ \\ \dashrightarrow \frak{-5x= 12 + 3x - 36} \\ \\ \dashrightarrow \frak{-5x - 3x= - 24} \\ \\ \dashrightarrow \frak{-8x = - 24} \\ \\ \star \quad \underline{ \boxed{ \green{ \frak{x = 3}}}} \\ \\ \underline{ \frak{ getting \: y}} : \\ \\ \dashrightarrow \frak{y = 3 - 12} \\ \\ \star \quad\underline{ \boxed{\blue{ \frak{y = - 9}}}} \\ \\ [/tex]

[tex] \green{ \mathbb{HENCEFORTH, \: THE \: PAIR \: IS \: \pink{\frak{ (3,-9)}}}}[/tex]


Some home computers can do a calculation in 2 x 10 ? seconds. Write this number in standard form.

Answers

☆Answer :

2 × 10 = 20

see Picture.

4. SCHOOL LUNCH In 2015, Ed spent $800 buying lunches. In 2017, he spent $300 buying lunches. What was the rate of change from 2015 to 2017?
A. –$250 per year
B. $125 per year
C. –$125 per year
D. $250 per year

Answers

Answer

B

Explanation

Mark Brainliest please

Write an equation with a slope of 2 and a constant of -5

Answers

y=mx+b

m is the slope, b is the constant.

y=2x-5

Use Pascal's Triangle to determine the sixth term of the expansion of (x + 5)^7

Answers

Pascal's triangle up to the 7th row (starting with 0)

1

1 1

1 2 1

1 3 3 1

1 4 6 4 1

1 5 10 10 5 1

1 6 15 20 15 6 1

1 7 21 35 35 21 7 1

Then the 6th term in the expansion of (x + 5)⁷ is

7 • x¹ • 5⁶ = 109375x

Answer soon please 10 points Easy math

Answers

Answer:

1 and -7

your first choice in the list

Step-by-step explanation:

yeah, this one was fun.

-6/5 - (-3/8)
Help please




Answers

Answer:

-0.825

Step-by-step explanation:

Did not know the options so do not know if this is right or not.

Here is ur answer.

- BRAINLIEST answerer

i need help friends on my math problem

Answers

Answer:

the answer is a

Hep help help help please please

Answers

Answer:

7,6

Step-by-step explanation:

Start from the horizontal line and then the vertical line

Answer:

according to the y and x axis rule the x comes first which means that 6 should go in the green box and 7 in the grey

Find the slope of the line that passes through:
(-12,-5) and (0, -8)

Answers

-3/12 because you can find the slope/m by doing the change of y over change of x

2 short questions
Please help

Answers

Answer:

b c = 5.25p this is the answer

For the first problem shown the answer is number B.

It is B because we our always going up by $5.25

For our second one it isn't a function,

it isn't a function because it follows the same rule through-out it besides at the end of it.

Does anyone know the solution

Answers

Answer and explanation in the image.

please help me with this

Answers

Answer:

14 Is a divident of 7 and 14

f(x)=x^2-(7/2)x-.5 and g(x)= 2-(2/x)

Answers

Answer:

23

Step-by-step explanation:

25.3 + x= 32 what is the answer to this problem

Answers

Answer:

6.7

Step-by-step explanation:

Answer:

6.700

Step-by-step explanation:

hope this helped

you will receive a golden cookie and 30 points if you help me

Answers

Answer:

A: -5/4 ; B: -0.5 ; C: 2

Step-by-step explanation:

Its the number line which shows.

Answer:

B = -0.5

A= -5/4

C= 2

Brainlest

Step-by-step explanation:

Which choices are equivalent to the expression below? Check all that apply.
4./6
O A. 96
B. 132.5
I C. 4../36
O D. 116.6
E. 196
OF V24
SUBMIT

Answers

Answer is
B 32 • 3
D 16•6
E 96
Square root them and multiply to get the answer

Can somebody answer this for me?

Answers

point slope form
standard equation: y-y1 = m(x-x1)
point given: (6,3)
slope given: 5/3
equation: y-3 = 5/3(x-6)
choice b

Given: passes though (6,3) and m=(5/3).

Ok so we know that y = mx + b is the equation of a line and we have m and we can find b via substitution.

y = mx + b

3 = (5/3)(6) + b

3 - (5/3)(6) = b

b = -7

Great now we know b so we can construct the rest of the linear function.

y = f(x) = (5/3)(x) - 7

You can always check the answer by plugging 6 into the x variable.

f(6) = (5/3)(6) - 7 = 3

(6,3) checks out.

How much flour and vanilla would you need for 5 batches of cookies

Answers

Answer:  25 cups of flour & 10 teaspoons of vanilla

Step-by-step explanation: A recipe for one batch of cookies calls for 5 cups of flour and 2 teaspoons of vanilla.

5 x 5 is 25 cups of flour

2 x 5 is 10 teaspoons of vanilla

Consider the following equation.

x+2y=4
Step 2 of 2 : Determine the missing coordinate in the ordered pair (?,12) so that it will satisfy the given equation.

Answers

X= -20

Substitute the value of y, which is 12, into the equation and solve for x.

X+2y=4
X+2(12)=4
X+24=4
-24 -24
——————
X=-20

An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?
13,200
26,400
39,600
79,200
158,400

Answers

Answer:

B) 26,400

An electrician must use 15 miles of electrical cable between electric poles. How many yards of cable will be used?

13,200

26,400

39,600

79,200

158,400

26400 yards of cable is used.

the answer is B) 26,400

What is unit conversion?

Unit conversion is the process of changing a physical quantity from one unit of measurement to another. For example, converting kilometers to miles, Celsius to Fahrenheit, or liters to gallons. The process involves multiplying or dividing the original measurement by a conversion factor, which is a ratio of equivalent units

To convert miles to yards, we need to multiply by the conversion factor of 1 mile = 1760 yards.

15 miles * 1760 yards/mile = 26,400 yards

So, the electrician will use 26,400 yards of cable.

Hence, 26400 yards of cable is used.

the answer is B) 26,400

To learn more about the unit conversion, visit:

https://brainly.com/question/97386

#SPJ1

The legs of a right triangle are √5 feet and square root √11 feet long. How long is the hypotenuse?

Answers

[tex]v^{2}[/tex]Answer:

4 feet long

Step-by-step explanation:

Pythagorean Theorem: [tex]a^{2}[/tex] + [tex]b^{2}[/tex] = [tex]c^{2}[/tex]

In this problem, a and b are the legs of the triangle, while c is the hypotenuse

Plugging the values of [tex]\sqrt{5}[/tex] and [tex]\sqrt{11}[/tex] to the equation you get:

5 + 11 = [tex]c^{2}[/tex]

Therefore, [tex]c^{2}[/tex] = 16, and by taking the square root you find that c, or the hypotenuse, must equal 4.

Evaluate the expression 61​

Answers

Answer:

61 + 8 is 69 and that is a funny number

Answer: if i get this correct mark me the brainlist promise

Step-by-step explanation:6+x=12To evaluate an algebraic expression, you have to substitute a number for each variable and perform the arithmetic operations. In the example above, the variable x is equal to 6 since 6 + 6 = 12.

Example

Calculate the following expression for x=3 and z=2

6z+4x=?

Solution: Replace x with 3 and z with 2 to evaluate the expression.

6z+4x=?

6⋅2+4⋅3=?

12+12=24

HELP PLEASE!!
Use the drop-downs to complete the sentences about this arithmetic sequence.
32, 41, 50, ...
The common difference is ___.
The fourth term is ______
The fifth term is ______

Answers

Answer:9,59,68

Step-by-step explanation:

Just got it right

please work QUICK its a test​

Answers

If you’re solving for d, it would be d = 10-3i

3) ) Each of the functions below model the monetary value of an item. Which is the only that has a growth factor showing the item is increasing in value? ​

Answers

Answer:

Imagine that scientists have just discovered a non-bird dinosaur skeleton. They want to know whether the dinosaur was closely related to birds. What features in ...

Step-by-step explanation:

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