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 .

answer: -8.2562234e+13

$9.41

step-by-step explanation: