Notation: Matrices A and B are said to be row equivalent, written A $$ B$,$ if matrix B can be obtained from matrix A by using ERO's.

Given A $=$ begin mathsize $20$px style open square brackets table row $13$ cell negative $4$ end cell row $15$ cell negative $1$ end cell row $313$ cell negative $6$ end cell end table close square brackets end style, M $=[$A I$],$ and the sequence of row equivalent matrices:

begin mathsize $20$px style open square brackets table row $13$ cell negative $4$ end cell $100$ row $15$ cell negative $1$ end cell $010$ row $313$ cell negative $6$ end cell $001$ end table close square brackets space rightwards arrow from E $2$ to E $1$ of space open square brackets table row $13$ cell negative $4$ end cell $100$ row $023$ cell negative $1$ end cell $10$ row $046$ cell negative $3$ end cell $01$ end table close square brackets space rightwards arrow with E $3$ on top open square brackets table row $13$ cell negative $4$ end cell $100$ row $023$ cell negative $1$ end cell $10$ row $000$ cell negative $1$ end cell cell negative $2$ end cell $0$ end table close square brackets space end style

Find the EROs in the steps; and the inverse A$-1,$ if defined..

$-$

E$1$

$-$

E$2$

$-$

E$3$

$-$

A$-1$

a$.$

$-$R$1+>$ R$2$

b$.$

NA

c$.$

Undefined

d$.$

begin mathsize $20$px style open square brackets table row $100$ row cell negative $1$ end cell $10$ row cell negative $1$ end cell cell negative $2$ end cell $1$ end table close square brackets end style

e$.$

begin mathsize $20$px style open square brackets table row $13$ cell negative $4$ end cell row $023$ row $000$ end table close square brackets end style

f$.$

$-$R$2+>$ R$3$

g$.$

$-3$R$1+>$ R$3$