Let A be a matrix, and let x and y be linearly independent vectors such that Ax=y, Ay=x+2y.Then we have that A^5 x=ax+by for some scalars a and b. Find the ordered pair (a, b).

Camila Brandt 2022-09-27 Answered
Let A be a matrix, and let 𝐱 and 𝐲 be linearly independent vectors such that 𝐀𝐱=𝐲,𝐀𝐲=𝐱+2𝐲.Then we have that A 5 x = a x + b y for some scalars 𝑎 and 𝑏. Find the ordered pair (a, b).
So far I have A 5 x = A 4 y
A 4 y = A 3 x + 2 A 3 y
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

Answers (2)

Miya Swanson
Answered 2022-09-28 Author has 11 answers
You were on the right track. Here are the next steps.
A 3 x = A 2 y and 2 A 3 y = 2 A 2 ( x + 2 y )
A 2 y = A A y = A ( x + 2 y ) and 2 A A x + 4 A A y = 2 A y + 4 A ( x + 2 y )
Can you take it from here?
Did you like this example?
Subscribe for all access
Jase Rocha
Answered 2022-09-29 Author has 2 answers
You are trying to reduce the powers, which works if you keep going. You can increase them as well. If A x = y and A y = x + 2 y, then
A 2 x = A ( A x ) = A y = x + 2 y A 2 y = A ( x + 2 y ) = A x + 2 A y = y + 2 ( x + 2 y ) = 2 x + 5 y A 3 x = A 2 y = 2 x + 5 y A 4 x = A 3 y = A ( 2 x + 5 y ) = 2 y + 5 ( x + 2 y ) = 5 x + 12 y
Did you like this example?
Subscribe for all access

Expert Community at Your Service

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

You might be interested in

asked 2021-05-29
Which of the following expressions are meaningful? Which are meaningless? Explain.
a) (ab)c
(ab)c has ? because it is the dot product of ?.
b) (ab)c
(ab)c has ? because it is a scalar multiple of ?.
c) |a|(bc)
|a|(bc) has ? because it is the product of ?.
d) a(b+c)
a(b+c) has ? because it is the dot product of ?.
e) ab+c
ab+c has ? because it is the sum of ?.
f) |a|(b+c)
|a|(b+c) has ? because it is the dot product of ?.
asked 2021-02-11
Let F be a fixed 3x2 matrix, and let H be the set of all matrices A in M2×4 with the property that FA = 0 (the zero matrix in M3×4). Determine if H is a subspace of M2×4
asked 2021-05-17
Find the scalar and vector projections of b onto a.
a=(4,7,4),b=(3,1,1)
asked 2021-05-29

Find the vector and parametric equations for the line segment connecting P to Q.
P(0, - 1, 1), Q(1/2, 1/3, 1/4)

asked 2021-06-04

Vectors V1 and V2 are different vectors with lengths V1 and V2 respectively. Find the following:
a) V1V1 Express you answer in terms of V1
b) V1V2, when they are perpendicular
c) V1V2, when they are parallel

asked 2021-11-13
Find the curl and of the vector field.
F(x,y,z)=(x+yz)i+(y+xz)j+(z+xy)k
asked 2021-09-03
Find a vector function that represents the curve of intersection of the two surfaces. The cylinder x2+y2=4 and the surface z=xy

New questions