Which of the following statements are true? If the equation Ax = b does not have

Question

Which of the following statements are true? If the equation Ax = b does not have a solution, then the matrix A is singular. The first entry in the product b = Ax is a sum of products. If the augmented matrix [A b ] does not have a pivot position in every row, then the matrix A is nonsingular. Any linear combination of n-vectors in R^n can always be written in the form Ax for a suitable matrix A and vector x. The equation Ax = b has a unique solution if and only if the matrix A is singular. An -vector b is a linear combination of the columns of an n times n matrix A if and only if the equation Ax = b has at least one solution.

Explanation / Answer

The equation Ax = b,

since matrix A is singular,then its determinent is 'zero'

hence A-1 DOES NOT EXIST,

There fore Ax = b does not have a solution.

hence option (A) is correct

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