can you explain reason for each answer? Which of the following statements are ne

Question

can you explain reason for each answer?

Which of the following statements are necessarily true? A. The first entry in the product Ax is a sum of products. B. If A is an m times n matrix whose columns do not span R^m, then the equation Ax = b is inconsistent for some b in R^m. C. The equation Ax = b is consistent if the augmented matrix [A | b] has a pivot position in every row. D. If the equation Ax = b is inconsistent, then b is not in the set spanned by the columns of A. E. Every matrix equation Ax = b corresponds to a vector equation with the same solution set. F. If the augmented matrix [A | b] has a pivot position in every row, then the equation Ax = b is inconsistent.

Explanation / Answer

A) true

Sometimes called a dot product. Uses the first row of A and the entries in x.

By definition of what matrix-vector multiplication means, the first entry in the product A~x is a11x1 + a12x2 + . . . + a1nxn, which is a sum of products.

B) TRUE

Saying that b is not in the set spanned by the columns of A is the same as saying that b is not a linear combination of the columns of A.

C) False.

if an augmented matrix has a pivot position in every row, the matrix may or may not be consistent.

D) TRUE

Saying that b is not in the set spanned by the columns of A is the same as saying that b is not a linear combination of the columns of A.

E)TRUE

Ax is simply a notation, a corresponding vector equation can be made.

F) FALSE

If a coefficient matrix has a pivot position in every row then Ax=b is consistent. However, for an augmented matrix, if there is a pivot position in every row Ax=b may or may not be consistent.

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.