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.

something that characterises a right triangle is the fact that we may use pythagoras' theorem to find any one of its sides given that we have the length of the other two sides. here, we have the length of the hypotenuse, √(87) yd, and one other side, √(23) yd, thus we can easily find the length of the remaining side using pythagoras' theorem as defined below:

c^2 = a^2 + b^2, where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

thus, given that c = √(87) and a = √(23), we may substitute these into the formula we defined above to get:

c^2 = a^2 + b^2

(√87)^2 = (√23)^2 + b^2 (substitute c = √87 and a = √23 into the equation)

87 = 23 + b^2 (evaluate (√87)^2 = 87 and (√23)^2 = 23 - remember that the square root of a number, squared will equal that very same number)

64 = b^2 (subtract 23 from both sides)

√64 = b (take the square root of both sides)

8 = b (evaluate √64 = 8)

therefor, the length of the unknown leg in the right triangle is 8 yd (first answer).