Question

Suppose you have an n×n homogenous linear system of equations. Make a statement classifying exactly when...

Suppose you have an n×n homogenous linear system of equations. Make a statement classifying exactly when you have a unique solution (what is it?) if the system is written in RREF. Prove (i.e. explain why) your statement is true.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Is it possible for a system of linear equations with more equations than unknowns to have...
Is it possible for a system of linear equations with more equations than unknowns to have a unique solution? What about fewer equations than unknowns? If your answer to either question is “yes,” provide an example.
Let A be a n × n matrix, and let the system of linear equations A~x...
Let A be a n × n matrix, and let the system of linear equations A~x = ~b have infinitely many solutions. Can we use Cramer’s rule to find x1? If yes, explain how to find it. If no, explain why not.
Is the following statement true or false: If a system of two linear differential equations is...
Is the following statement true or false: If a system of two linear differential equations is saddle point stable, the variables can move against their steady state values ​​over time. Explain your answer.
The augmented matrix represents a system of linear equations in the variables x and y. [1...
The augmented matrix represents a system of linear equations in the variables x and y. [1 0 5. ] [0 1 0 ] (a) How many solutions does the system have: one, none, or infinitely many? (b) If there is exactly one solution to the system, then give the solution. If there is no solution, explain why. If there are an infinite number of solutions, give two solutions to the system.
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...
A system of linear equations is said to be homogeneous if the constants on the right-hand...
A system of linear equations is said to be homogeneous if the constants on the right-hand side are all zero. The system 2x1 − x2 + x3 + x4 = 0 5x1 + 2x2 − x3 − x4 = 0 −x1 + 3x2 + 2x3 + x4 = 0 is an example of a homogeneous system. Homogeneous systems always have at least one solution, namely the tuple consisting of all zeros: (0, 0, . . . , 0). This solution...
A linear system of equations Ax=b is known, where A is a matrix of m by...
A linear system of equations Ax=b is known, where A is a matrix of m by n size, and the column vectors of A are linearly independent of each other. Please answer the following questions based on this assumption, please explain it, thank you~. (1) To give an example, Ax=b is the only solution. (2) According to the previous question, what kind of inference can be made to the size of A at this time? (What is the size of...
Prove that for a square n ×n matrix A, Ax = b (1) has one and...
Prove that for a square n ×n matrix A, Ax = b (1) has one and only one solution if and only if A is invertible; i.e., that there exists a matrix n ×n matrix B such that AB = I = B A. NOTE 01: The statement or theorem is of the form P iff Q, where P is the statement “Equation (1) has a unique solution” and Q is the statement “The matrix A is invertible”. This means...
For each part below, give an example of a linear system of three equations in three...
For each part below, give an example of a linear system of three equations in three variables that has the given property. in each case, explain how you got your answer, possibly using sketches. (a) has no solutions (b) has exactly one solution which is (1, 2, 3). (c) any point of the line given parametrically be (x, y, z) = (s − 2, 1 + 2s, s) is a solution and nothing else is. (d) any point of the...
True False questions. Make sure you EXPLAIN EACH ANSWER. 2.19) Suppose that W is a four-dimensional...
True False questions. Make sure you EXPLAIN EACH ANSWER. 2.19) Suppose that W is a four-dimensional subspace of R7 that is spanned by {X1,X2,X3,X4}. Then one of the Xi must be a linear combination of the others. 2.20)Suppose that A is a 3 x 5 matrix such that the vectors X = [1,1,1,1,1]^t, Y= [0,1,1,1,1]^t, and Z = [0,0,1,1,1]^t belong to the nullspace of A. 2.20a) The rows of A are dependent. 2.20b) AX= B has a solution for all...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT