# Using Determinant

1. Nov 22, 2007

### salman213

Hi, I have a midterm tomorrow for my Lin Alg course and I was doing some review probs and I cant seem to understand this one..

Can someone help me and explain how to do this one!!

I know I can just find the whole vector

x1,x2,x3,x4 by just multiplying by A^-1 but on a midterm I dont thinK I will want to waste time and find the inverse of such a matrix if there is another way to approach this problem.

2. Nov 22, 2007

### HallsofIvy

Staff Emeritus
IF you knew A-1, then x3 would just be third row of A-1 time that vector- in other words, since the given vector has a 1 in the second place, zeros elsewhere, it would be the number in the third row, second column of A-1. Can you think of a way of finding that number only? (Especially since you are given the determinant!)

3. Nov 22, 2007

### salman213

thanks a lot

Cof (a) (2,3)
------------ = would be that specific element
det a

right?
!!

4. Nov 23, 2007

I'm not sure what you mean by "cof(2,3)", but, since you're given a Cramer system AX = B (A is a regular matrix), the solution is X = (x1, x2, x3, x4), where xi = Dj / D, where Dj is the determinant of the matrix which is created by substituting the j-th column of the matrix A with B, and D = det A.

5. Nov 23, 2007

### salman213

Yea somone asked that question today in morning cause exam is in afternoon and he said to do it that way ur saying.. so i guess i get what u said thanks!

but i treid what i was saying and it gives same answer since basically Cofactor of A of the 2,3 term divided by determinant of A is exactly the 3,2 term in the A^-1 and therefore thas waht we want. It gives same answer so I guess you can do it etiehr way but im sure he would want us to use cramers rule to get like ur saying

det A with 3rd column replaced with 0,1,0,0 over determinant of A

thanks!