Let Ab e an invertiblen×nmatrix, and let B be ann×pmatrix. Show thatthe equationAX=Bhas a unique solutionA−1B. Hint: You need to show thatA−1Bis a solution, and that there is no other solution. You might do this secondpart by making an argument each column ofB

In fact,  is a solution to the equation AX = B. Let me show you.

Step-by-step explanation:

Step 1 .

Remember that there's a very special x matrix, called "the identity matrix", we denote it as .

That matrix is special because

                                    *(Any matrix)  = Any matrix,

So, when I say, "Any matrix", that literally means, "Any martrix", well, any x matrix. Therefore;

                                                     *A = A

Step 2.

Remember that A is invertible if there exist a matrix such that

                                                      * =   .

 is just the name of it, the most important is the property I just mentioned.

Step 3.

Now, to show that,  we just have to show that is a solution of , in other words we have to show that,  

Notice that

Therefore, is a solution of .

from the figure we get,

the x axis shows   the months and,

the y-axis shows the number of satisfied customer.

each line or each cell in upward direction (y-axis) shows 500.

the appropriate scale for the y - axis is: -

a = 2000 customers

b = 4000 customers

c = 6000 customers

d = 8000 customers

e = 10000 customers

f = 12000 customers

g = 14000 customers

square root of 36/6 = 2.449489743

square root of 16/6 = 1.632993162

square root of 6 = 2.449489743

the answer is square root of 16/6 because the square root of 36/6 is the same answer as square root of 6 = 2.449489743