Ascientist solves a nonhomogeneous system of ten linear equations in twelve unknowns and finds that three of the unknowns are free variables. can the scientist be certain that, if the right sides of the equations are changed, the new nonhomogeneous system will have a solution? discuss.

No, scientist can't be certain that, if the right sides of the equations are changed, the new non homogeneous system will have a solution.

Step-by-step explanation:

Consider the system .

Where A is given matrix

A non homogeneous system of ten linear equations in twelve unknowns and finds that three of the unknowns are free variables.

Here the given matrix is a 10×12 matrix.

It is given that three of the unknown are free variable, that means the dimension of null A is 3.

The rank of the matrix is:

Since, the rank of the matrix is 9 and there are 10 equations that means the system cannot have a solution for all "b".

Therefore, the system is inconsistent.

No, scientist can't be certain.

answer:

it is general formula that is used to write value to its excet position

a11 a12 a13

a21 a22 a23

it is the example of order 2 by 3 matrix in this

a11 means value occur in 1 st row 1st column

a12 means value occurs in 1st row 2nd column

a13 means value occur in 1st row and 3rd column

a21 means value occurs in 2nd row and 1st column

a22 means value occurs in 2nd row and in 2nd column

a23 means value occurs in 2nd row and in 3rd column

correct choice is b

step-by-step explanation:

when you calculate the average rate of change of a function, you are finding the slope of the secant line between the two points. for the function the average rate of change from point to point can be calculated as

to find the average rate of change from day 2 to day 10, note that at day 2, 8 houses were sold, so a(2,8) and at day 10, 2 houses were sold, so b(10,2). thus,