Suppose the augmented matrix for a given system has a pivot in every column. say as much as you can about the solutions to the corresponding system of equations, with explanation.

The system is inconsistent.

Step-by-step explanation:

Consider the provided information.

The augmented matrix for a given system has a pivot in every column.

Let us understand this fact with the help of an example.

Suppose an 8 × 6 augmented matrix has a pivot in every column.

The above matrix is augmented and has a pivot in every  column, that means the rightmost column in the above matrix must be a pivot column.

The rightmost column of the above matrix will be something like this:

0 0 0 0 0 | b

Where b≠0 because if b is 0 then it can't be a pivot position.

But from the above 0 = b, which is false.

This means  that the system is not consistent,

Hence, the system is inconsistent.

sine

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: