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qwelly [4]
3 years ago
8

) The points (1, 0, 3), (1, 1, 1), and (−2, −1, 2) lie on a unique plane a1x1 + a2x2 + a3x3 = b. Using your previous answers, fi

nd an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

Mathematics
2 answers:
Rudik [331]3 years ago
6 0

Answer:

x1-2x2-x3= -2

Step-by-step explanation:

Substitute the three points to get three equations:

a1+0a2+ 3a3=d --------------eq i

a1+a2+a3=d----------------eq ii

-2a1-a2+2a3=d---------------eq iii

subtract eq i from eq ii

a2-2a3=0 ----------- eq iv

now add eq iv to eq iii

-2a1=d ------- eq v

put eq v in eq i

a1 + 3a3=-2a1

a3=  -a1 ----------- eq vi

put eq vi in eq iv

a2-2(-a1)=0

a2= -2a1 ------ eq vii

put eq v, eq vi and eq vii in the equation of plane

a1x1+ a2x2+a3x3=d

a1x1 -2a1x2-a1x3=-2a1

x1-2x2-x3= -2

Akimi4 [234]3 years ago
6 0

Answer:

2x₁ - x₂ + x₃ = 2

Question in full

(a) Find the general solution for the following system of linear equations:

z2 + 3z3 − z4 = 0

−z1 − z2 − z3 + z4 = 0

−2z1 − 4z2 + 4z3 − 2z4 = 0

(b) Give an example of a solution to the previous system of linear equations.

(c) The points (0, 1, 3), (1, 1, 1), and (−1, −2, 2) lie on a unique plane in R 3 , defined by an equation of the form a1x1 + a2x2 + a3x3 = b. Using your previous answers, find an equation for this plane. (Hint: think about the relationship between the previous system and the one you would need to solve in this question.)

Step-by-step explanation:

The augmented matrix is \left[\begin{array}{ccc}1&2&3&0\\4&5&6&0\\7&8&9&0\end{array}\right]

The echelon form

The general solution and the sample solution

as well as the equation of the plane

are given in the attached solution below

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sergiy2304 [10]

Answer:

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Step-by-step explanation:

Let us use the ratio method to solve the question

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∴ The drawing length of the room = 8 inches

∴ The drawing width of the room = 6 inches

→ By using the ratio method

→  inches  :  feet

→  1            :  3

→  8           :  L

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→ By using the cross multiplication

∵ 1 × L = 8 × 3

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∴ The actual width of the room is 18 feet

Use the formula of the area of the rectangle to find the area of the room

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A resturant sells 10 tacos for 8.49,or 6 of the same kind of taco for 5.40.Which is a better deal
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Which of the following statements are true?
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A, B, and C are all true.

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We need to subtract 10 1/4 from 26 1/3 to get the fraction of the space not covered by the towel bar. 
We also need to divide the difference by 2 because we placed the towel bar in the center of the door.

1st we need to convert the mixed fractions into fractions to perform subtraction.
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Steps in Subtracting Fractions
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Step 2. Subtract the numerators and place them above the common denominator
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Before we can simplify the fraction, we must divide it by two to get the measurement of each edge of the door.

Steps in dividing fractions.
Step 1. Get the reciprocal of the 2nd fraction.
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Step 2. Multiply the 1st fraction to the reciprocal of the 2nd fraction
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Step 3. Simplify the fraction.
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