-2x1 +3x2 + mx3 =5
2x1 –3x2 - 4x3 = -7
-X1 + 2x2+2x3 = 2

Rewrite the system in the format Ax = b and determine the following:

a. Find the value for m such that det(A) = |A| = 1 using cofactor expansion along the first row (R1).
b. Based on the given value of the determinant, identify the type of system (consistent/inconsistent) and the corresponding number of solutions.
c. Based on the given value of the determinant, how many row/column vectors of A are independent and what is their span?
D. Using your m value from part A, determine the following:

a. Find the following cofactors: C21, C22, C23
b. Find the inverse of A using MATLAB. Write down everything you typed into MATLAB to find the inverse, including your A matrix. Identify on your paper where your cofactors are located in the inverse.
c. Solve the system of equations using the inverse of A.

Suppose we have a set of small wooden blocks showing the 26 letters of the english alphabet, one letter per block. (think of scrabble tiles.) our set includes 10 copies of each letter. we place them into a bag and draw out one block at a time. (a) if we line up the letters on a rack as we draw them, how different ways coukl we fill a rack of 5 letters? (b) now suppose we just toss our chosen blocks into a pile, and whenever we draw a letter we already have, we put it back in the bag and draw again. how many different piles of 5 blocks could result? possible? piles will contain at least one repeated letter? (c) if we draw out 5 blocks wit hout looking at them, how many different piles are (d) if we draw out 5 blocks without looking at them, how many of the possible 2. (4) consider the following formula. 12 give two different proofs, one using the factorial formulas and the other combina torial.