Question

solve this problem about matrix:--

Answer 1

if [A] is a matrix, then-

Answer 2

what is the matrix?????????

Answer 3

\[[A]=\left[\begin{matrix}1 & 0 \\ -1 & 7\end{matrix}\right]\]

Answer 4

then prove that \[A^2-8A+7I=0\]

Answer 5

its so simple

Answer 6

firstly multiply A with A

Answer 7

YOU KNOW HOW TO MULTIPLY TWO MATRICES OR SHOULD I SHOW YOU

Answer 8

yeah K! I know this method which u r telling but my real doubt is that "isn't there a short trick method for proving it .Please tell

Answer 9

2) MULTIPLY EACH ELEMENT OF MATRIX A BY 8

Answer 10

k! then

Answer 11

3) MULTIPLY 7 WITH EACH ELEMENT OF IDENTITY MATRIX

Answer 12

THEN WHAT SUBTRACT THE MATRICES OBTAINED IN 1ST AN 2ND STEP AND ADD THE RESULTANT MATRIX WITH THAT OBTAINED IN THIRD STEP

Answer 13

k! but Here ,My real doubt is that "isn't there a short trick method for proving it" .Please tell me.

Answer 14

THERE IS NO SHORTCUT TO SUCH PROBLEMS

Answer 15

K! if i tell u a short trick that my sir did then

Answer 16

OK WHICH ONE

Answer 17

SO MR IF YOU KNOW THE ANSWER THEN ARE YOU TESTING OTHERS KNOWLEDGE

Answer 18

SO WHATS THE METHOD

Answer 19

firstly there is a rule \[|A-\lambda I|\] put the values here

Answer 20

& get a determinant & when we solve that determinant than we get a polynomial in the form of \[\lambda\].

Answer 21

now we put A instead of lambda.& get the above result:)

Answer 22

Yes, latent roots are trickier way and probably the only logical way for doing this.

Answer 23

@nitz: All caps is considered yelling in virtual world. Please avoid using that.

Answer 24

WHICH CAP

Answer 25

ALL UPPER CASE, all lower case.

Answer 26

OK

Answer 27

ok! thanx to u both but did u get it @nitz

Answer 28

@maheshmeghwal9: If you are not aware of it, this is due to cayley-hamilton theorem.

Answer 29

and I wanna know another short trick please tell

Answer 30

YA

Answer 31

K!

Answer 32

FOR YOUR INFORMATION I HAVE READ A BOOK ON MATRICES AND DETERMINANTS AN I KNOW ALL THIS CAYLEY HAMILTON THEOREM ETC.
@FOOL FOR MATH

Answer 33

k! thanx to both hope I could give u both medals.

Answer 34

coz I can't do partiality.

Answer 35

i am sorry if you people thought i was rude
extremely sorry

Answer 36

np:)

Answer 37

what do you do