claywatts

第11題點計?
I 等如 ( 2  2)   ?
             -1 3

Simon

樓主不知道什麼是I ?

kiwakwok

I refers to the identity matrix. You may look up the definition in your textbook.

[ 本帖最後由 kiwakwok 於 2011-4-14 10:38 PM 編輯 ]

claywatts

I = ( 1 0 )  
        0 1

claywatts

之後點計?

桃子

Identity matrix is a matrix with entries 1 on the diagonal and 0 elsewhere.

Simon

If you know A^2, then you can do all stuff

kiwakwok

Have you learnt matrix multiplication?

claywatts

A^2 - 7A  +14I

=( -14  0  )  + 14( 1  0 )
      0   -14             0  1

=0
thank you so much

jinjin06

A^2 = (7   14)    or  7(1  2)
           -7   14             -1  2

A^2 - 7A = 7[(1-3)    (2-2)]       = 7 (-2    0)  or   = -14 (1   0)
                      (-1+1)  (2-4)               0     -2                   0    1

final ans = 0

桃子

A zero matrix is different from a scalar 0.

kilinho123

I=(0 0)
     0 0
  A^2-7A+14I=(7 14) - (21 14) + (14 0)
                        -7 -14     -7  28        0 14
                      =0

[ 本帖最後由 kilinho123 於 2011-4-15 06:30 PM 編輯 ]

桃子

Same problem

A zero matrix is different from a scalar 0.

pphh

Yes, Don't confuse zero matrix with scalar value 0. They are completely different !!! Be very careful on writing.

kin1205

A,B is two matrices in same order,
if cA+dB = eI,  where c,d,e are constants
how to prove AB=BA ? Thanks