Question

Let A be a given (3 × 3) matrix, and consider the equation Ax = c,...

Let A be a given (3 × 3) matrix, and consider the equation Ax = c, with c = [1 0 − 1 ]T . Suppose that the two vectors x1 =[ 1 2 3]T and x2 =[ 3 2 1] T are solutions to the above equation.

(a) Find a vector v in N (A).

(b) Using the result in part (a), find another solution to the equation Ax = c.

(c) With the given information, what are the possible values for null(A)?

Math   Advanced-Math   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T...
Find the matrix A in the linear transformation y = Ax,where a point x = [x1,x2]^T is projected on the x2 axis.That is,a point x = [x1,x2]^T is projected on to [0,x2]^T . Is A an orthogonal matrix ?I any case,find the eigen values and eigen vectors of A .
Let A be an m×n matrix, x a vector in Rn, and b a vector in...
Let A be an m×n matrix, x a vector in Rn, and b a vector in Rm. Show that if x1 in Rn is a solution to Ax=b and x2 is a solution to Ax=⃗0, then x1 +x2 is a solution to Ax=b.
Given a matrix A, the equation Ax=b might have 0 solutions for all b, or 1...
Given a matrix A, the equation Ax=b might have 0 solutions for all b, or 1 solution for all b, or 0 solutions for some choices of b and 1 solution for others, or 0 solutions for some choices of b and ∞ solutions for others, or 1 solution for some b and ∞ solutions for others, or 0,1, or ∞ solutions for different choices of b. (7 different combinations in all.) Which of these combinations are actually possible? Justify...
Find the standard matrix for the following transformation T : R 4 → R 3 :...
Find the standard matrix for the following transformation T : R 4 → R 3 : T(x1, x2, x3, x4) = (x1 − x2 + x3 − 3x4, x1 − x2 + 2x3 + 4x4, 2x1 − 2x2 + x3 + 5x4) (a) Compute T(~e1), T(~e2), T(~e3), and T(~e4). (b) Find an equation in vector form for the set of vectors ~x ∈ R 4 such that T(~x) = (−1, −4, 1). (c) What is the range of T?
4. Suppose that we have a linear system given in matrix form as Ax = b,...
4. Suppose that we have a linear system given in matrix form as Ax = b, where A is an m×n matrix, b is an m×1 column vector, and x is an n×1 column vector. Suppose also that the n × 1 vector u is a solution to this linear system. Answer parts a. and b. below. a. Suppose that the n × 1 vector h is a solution to the homogeneous linear system Ax=0. Showthenthatthevectory=u+hisasolutiontoAx=b. b. Now, suppose that...
Let ? be an ?×? matrix, and consider the equation ??⃗ = 0⃗. Show that for...
Let ? be an ?×? matrix, and consider the equation ??⃗ = 0⃗. Show that for any ?⃗ ∈ ℝ?, the solution of the equation ??⃗ = 0⃗ which minimizes the distance between ?⃗ and ?⃗ is given by ?⃗ = ?⃗ − ???⃗ where ????⃗ = ??⃗ .
Find the (real-valued) general solution to the system of ODEs given by: X’=[{-1,-1},{2,-3}]X (X is a...
Find the (real-valued) general solution to the system of ODEs given by: X’=[{-1,-1},{2,-3}]X (X is a vector) -1,-1, is the 1st row of the matrix 2,-3, is the  2nd row of the matrix. Then, determine whether the equilibrium solution x1(t) = 0, x2(t) = 0 is stable, a saddle, or unstable.
Let V be the subspace of all vectors in R 5 , such that x1 −...
Let V be the subspace of all vectors in R 5 , such that x1 − x4 = x2 − 5x5 = 3x3 + x4 (a) Find a matrix A with that space as its Null space; What is the rank of A? b) Find a basis B1 of V ; What is the dimension of V ? (c) Find a matrix D with V as its column space. What is the rank of D? To find the rank of...
Consider a plane and a line given by equation ax + by = 0. Write a...
Consider a plane and a line given by equation ax + by = 0. Write a 2×2 matrix, M, of the mirror reflection (flip) around this line. Calculate det(M) and M2 and discuss the results.
Find the fundamental matrix solution for the system x′ = Ax where matrix A is given....
Find the fundamental matrix solution for the system x′ = Ax where matrix A is given. If an initial condition is provided, find the solution of the initial value problem using the principal matrix. A= [ 4 -13 ; 2 -6 ]. , x(o) = [ 2 ; 0 ]
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT