Which of the following statements are true? Remember that a mathematical statement is said to be true if it is always true, under all circumstances. A. Every matrix equation Ax b corresponds to a vector equation with the same solution set.
B. If A is an m x n matrix and if the equation Axb is inconsistent for some b in R", then A cannot have a pivot in every row.
C. The first entry in the product Ax is a sum of products.
D. If the augmented matrix [A l b] has a pivot position in every row, then the equation Ax-b is inconsistent.
E. The equation Ax-b is consistent if the augmented matrix [A I b] has a pivot position in every row.
F. If A is an m x n matrix whose columns do not span Rm, then the equation Ax-b İs inconsistent for some b in R.

A, B, C, F

Step-by-step explanation:

Statement A is true.

All the matrix equation of the order always corresponds to any vector equation having the same solution set.

Statement B is true.

If P is any matrix of the order m x n and if the equation  is inconsistent for any b in , then P does not have a pivot in all the rows.

Statement C is true.

The first entry of elements in a product Ax is the sum of the products.

Statement F is true.

If a matrix A of order m x n and whose columns does not span   , then equation  will be inconsistent for any b in .

answer: you need the equation in the question so i can answer it

step-by-step explanation:

constant of proportionality = 3 and the equation is c = 3p.

step-by-step explanation:

c = kp   where c = amount of caffeine in mg., p = oz of pepsi and k is the constant of proportionality.

substituting the values given:

24 = 8k

k = 3.

the same value of k will be obtained if we substitute the other given values.