Question

Let A be an nxn matrix. Show that if Rank(A) = n, then Ax = b...

Let A be an nxn matrix. Show that if Rank(A) = n, then Ax = b has a unique solution for any nx1 matrix b.

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
Let A be an nxn matrix. Prove that A is invertible if and only if rank(A)...
Let A be an nxn matrix. Prove that A is invertible if and only if rank(A) = n.
Let A,B be a m by n matrix, Prove that |rank(A)-rank(B)|<=rank(A-B)
Let A,B be a m by n matrix, Prove that |rank(A)-rank(B)|<=rank(A-B)
Let P be an nxn projectionmatrix with the columnspace W(n geq 2). Define the matrix A...
Let P be an nxn projectionmatrix with the columnspace W(n geq 2). Define the matrix A as: A=2P-I. Show that A has no other eigenvalues than 1 and -1.
Suppose we are given a system Ax = b, with A an n × m matrix....
Suppose we are given a system Ax = b, with A an n × m matrix. What can you say about the solution set of the system in the following cases? Provide a brief explanation. (i) rank(A) < n (ii) rank(A) = n (iii) rank(A) < m (iv) rank(A) = m
In the system AX=b, where A is m x n matrix and rank of A is...
In the system AX=b, where A is m x n matrix and rank of A is m, you are given n vectors and among them p vectors are linearly dependent (p > m). Please write down the procedure to reduce the number of dependent vector by 1.
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.
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...
Let A be an m × n matrix, and Q be an n × n invertible...
Let A be an m × n matrix, and Q be an n × n invertible matrix. (1) Show that R(A) = R(AQ), and use this result to show that rank(AQ) = rank(A); (2) Show that rank(AQ) = rank(A).
Suppose A ∈ Mm×n(R) is a matrix with rank m. Show that there is an n...
Suppose A ∈ Mm×n(R) is a matrix with rank m. Show that there is an n × m matrix B such that AB = Im. (Hint: Try to determine columns of B one by one
Let A be square matrix prove that A^2 = I if and only if rank(I+A)+rank(I-A)=n
Let A be square matrix prove that A^2 = I if and only if rank(I+A)+rank(I-A)=n
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT