SOLUTION: suppose A is a 3x3 matrix with elements a11 =1 a12=0 a13=2 a21=-1 a22=3 a23=4 a31=0 a32=1 a33=0 how would you use A^-1 to find the solutions of the linear system x+2z = 1 and

Question 350586: suppose A is a 3x3 matrix with elements
a11 =1 a12=0 a13=2
a21=-1 a22=3 a23=4
a31=0 a32=1 a33=0
how would you use A^-1 to find the solutions of the linear system
x+2z = 1 and -x+3y+4z =2 and y=3
could you please show working.
i have used numbers with subscripts to depict the matrix entries because i dont know how to type the brackets
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
[A]=
.
.
.
[A][x]=[b]
.
.
where,
[x]=
[b]=
.
.
.
[A][x]=[b]
.
.
[A]inv[A][x]=[A]inv[b]
.
.
Since [A]inv[A]=[I], then
.
.
[x]=[A]inv[b]
.
.
.
det[A]=
.
.
.
[A]inv=
*([A]inv[b])=
*([A]inv[b])=
Then,
[x]=
RELATED QUESTIONS
Let A = a11 a21 a11 a12 a22 a12 a13 a23 a13 where aij eR for each 1<=i;j<=3: Which... (answered by richard1234)

Let A = a11 a21 a11 a12 a22 a12 a13 a23 a13 where aij 2R for each 1<=i;j<=3: Which... (answered by richwmiller)

A. Create matrix A such that a11=4, a12=6, a21=0, and a22=-1. B. What is the additive... (answered by jim_thompson5910)

calcule: 3 9 1 1 2 5 1 -1 0 a)A12 b)A23 c)A33 (answered by Fombitz)

calcule: 1 -1 2 5 7 -4 1 0 1 a)A23 b)A13 c)A23 (answered by Fombitz)

Here is my last question.Thanks in advanced for your help:) Question: Let A be a 2... (answered by robertb)

how do you identify the indicated elements for example a32 A= 3 12 6 1 0 9 (answered by stanbon)

Refer to matrix A and identify the matrix element a12 A= [0 -1] 1.5 3 7... (answered by jim_thompson5910)

Evaluate the following determinants. This is a 3x3 matrix. the 3 is outside of the... (answered by Jk22)