The system of equations may have a unique solution, an infinite number of solutions, or no solution. use matrices to find the general solution of the system, if a solution exists. (if there is no solution, enter no solution. if there are infinitely many solutions, express your answers in terms of z as in example 3.) 5x + 4y + 5z = −1 x + y + 2z = 1 2x + y − z = −3

Infinite number of solutions.

Step-by-step explanation:

We are given system of equations

Firs we find determinant of system of equations

Let a matrix A= and B=

Determinant of given system of equation is zero therefore, the general solution of system of equation is many solution or no solution.

We are finding rank of matrix

Apply and

:

Apply

:

Apply

:

Apply and

:

Apply

:

Rank of matrix A and B are equal.Therefore, matrix A has infinite number of solutions.

Therefore, rank of matrix is equal to rank of B.

There is sufficient evidence to support the claim that the standard deviation of time all women spend washing their hair in the morning is 15 seconds

=================================================

Explanation:

First focus on "You find the initial conclusion of your test fails to reject the null hypothesis"

The key thing to pull out from that is "fail to reject the null hypothesis". Failing to reject means we basically "accept", more or less, the null. We have no other choice until more data comes along to reject the null.

The claim is " the standard deviation of time all women spend washing their hair in the morning is 15 seconds." which is where the null hypothesis is made. In terms of symbols, we would write . The alternate hypothesis is . The symbol is the greek letter sigma that represents the population standard deviation.