asked in category: General Last Updated: 24th February, 2020

# What is Ax B when does Ax B has a unique solution?

Let A be a square n × n matrix. Then Ax = b has a unique solution if and only if the only solution of Ax = 0 is x = 0. Let A = [A1,A2,,An]. A rephrasing of this is (in the square case) Ax = b has a unique solution exactly when {A1,A2,,An} is a linearly independent set.

Also know, does Ax B have a solution?

Ax = b has a solution if and only if b is a linear combination of the columns of A. Note: If A does not have a pivot in every row, that does not mean that Ax = b does not have a solution for some given vector b. It just means that there are some vectors b for which Ax = b does not have a solution.

Similarly, what is a in Ax B? Definition. If A is an m n matrix, with columns a1,a2,,an, and if x is in Rn, then the product of A and x, denoted by Ax, is the linear combination of the columns of A using the corresponding. entries in x as weights.

Beside above, what is the solution to the equation Ax B?

A vector b is a linear combination of the columns of a matrix A if and only if the equation Ax=b has at least one solution. T/F? True. The equation Ax=b has the same solution set as the equation x(1) a(1) + x(2) a(2) +

Is the system Ax B solvable for each B in r3?

combination of the columns of A, there is no solution to Ax = b. If r = m, then the reduced matrix R = I F has no rows of zeros and so there are no requirements for the entries of b to satisfy. The equation Ax = b is solvable for every b.

### What is a pivot position?

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24th February, 2020

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