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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.

Respuesta :

Answer:

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 [tex]$Px=b$[/tex]  is inconsistent for any b in [tex]$R^m$[/tex] , 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  [tex]$R^m$[/tex] , then equation [tex]$Ax=b$[/tex]  will be inconsistent for any b in [tex]$R^m$[/tex] .

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