Find all scalars c_{1} , c_{2}, c_{3} such that c_{1}(1 , -1, 0) + c_{2}(4, 5, 1) + c_{3}(0, 1, 5) = (3, 2, -19)

beljuA 2021-03-11 Answered
Find all scalars c1,c2,c3 such that c1(1,1,0)+c2(4,5,1)+c3(0,1,5)=(3,2,19)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

Nathanael Webber
Answered 2021-03-12 Author has 117 answers
The equation c1(1,1,0)+c2(4,5,1)+c3(0,1,5)=(3,2,19)
becomes (c1c1,0)+(4c2,5c2,c2)+(0,c35c3)=(3,2,19)
which can be written as (c1+4c2,c2+5c2+c3,c2+5c3)=(3,2,19)
This gives us the the system c1+4c2=3
c1+5c2=c3=2
c2+5c3=19
From the first equation we get c1=34c2
From the third equation we get c2=195c3
Thus, c1=34c2=34(195c3)+c3=244c3174=2
This yields 44c3=176c3=4
Thus, c2=195c3=195(4)c2=1
and c2=79+20c3=79+20(4)c1=1
Therefore, to conclusude, c1=1,c2=1,c3=4
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-05-14
Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R
b) Find the area of the triangle PQR
asked 2021-06-01
Find the vectors T, N, and B at the given point.
r(t)=<t2,23t3,t> and point <4,163,2>
asked 2021-09-22

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at (1,3,0),(2,0,2),and(1,3,1).

asked 2021-09-05
The average height of a 2 year old boy is 38 inches. an 8 year old averages 56 inches. Use this information to write a linear equation that models the height (in inches), y, in terms of the age (in years), x. Use the linear equation to predict the average height of a 5 year-old boy.
asked 2021-09-19
v is a set of ordered pairs (a, b) of real numbers. Sum and scalar multiplication are defined by: (a, b) + (c, d) = (a + c, b + d) k (a, b) = (kb, ka) (attention in this part) show that V is not linear space.
asked 2022-01-21
For what value of λ the following vectors will form a basis for E3.
a1=(1,5,3),a2=(4,0,λ),a3=(1,0,0)?
asked 2021-11-03

Consider the following.

z = x2 + y2,   x = 5s + 6t,   y = s + t

Find 

z
s

 and 

z
t

 by using the chain rule. (Enter your answers in terms of s and t.)

z
s

=

52s+62t

 

z
t

=

62s+74t

 

Find 

z
s

 and 

z
t

 by first substituting the expressions for x and y to write z as a function of s and t. (Enter your answers in terms of s and t.)

z
s

=

 

 

z
t

=

 

Do your answers for 

z
s

 agree?

YesNo    

Do your answers for 

z
t

 agree?

YesNo