This is a set of corrections for a midterm, no one in the class managed to get m

Question

This is a set of corrections for a midterm, no one in the class managed to get more than two of these correct, which I did accomplish. We were warned that MANY of the letters may apply to one of these questions. I'd like to understand which of these are correct and why. Thanks.

3 pts each) For each question, give the correct answers from a-l regarding WHAT MUST BE TRUE. List all correct answ this question. Again - only list letters for WHAT MUST BE TRUE. You do not have to explain your answers. AX b is a linear system. Assume that dimensions of A, x, b are appropriate. 1. A is a square matrix. 2. A is a non-singular ma 3. A is a singular matrix 4. A is a non-singular matrix and b is zero 5. A has more rows than columns and b is zer 6. A has more columns than row 7. A has more columns than rows and the rank of A is equal to the number of rows. , are appropriate. l J. Check 8. A has more rows than columns and the rank of A is equal to the number of columns 9. The row rank of A is equal to th equal to the number of columns 10. A has more columns than rows and the rank of A is less than the number of rows and b is zero a) there is no solutien b) there is exactly one solution, which must be the zero vector c) there is exactly one solution, which must be a non-zero vector d) there is exactly one solution, and we cannot determine from the information whether it s zero e) there are an infinite number of solutions f) there are either 0 or an infinite number of solutions g) there are either 1 or an infinite number of solutions h) there are either 0 or 1 solutions i) there are either 0, 1, or an infinite number of solutions j) the matrix A has a determinant k) the matrix A does not have a determinant 1) we cannot determine whether the matrix A has a determinant rows and the column rank of A is I J, Check

Explanation / Answer

1. I,j

As a square matrix has determinant and the system Ax=b may have a unique, no or infinitely many solutions

2. J,d

That solution may be trivial or non trivial

3. J,f

The solutions would be inconsistent or consistently infinite

4. J,b

In this case the solution would be trivial

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