Suppose A is aa 2x2 matrix with real number entries,

FInd such A that A^2=-I, where I is the 2x2 identity matrix
@amistre64

Question

Suppose A is aa 2x2 matrix with real number entries,

FInd such A that A^2=-I, where I is the 2x2 identity matrix
@amistre64

caozeyuan · Answer

@RosieS12  Hey there, any idea for this one?

anonymous · Answer

well i think we have to find what x and y equal and then plug them in the equation?

caozeyuan · Answer

what do you mean x and y?

anonymous · Answer

oh im really sorry i was looking at the wrong question xc my bad :)

amistre64 · Answer

a b   a b      -1  0
c d   a b  =   0  -1

aa + ab = -1
ac + ad = 0
ba + db = 0
bc + dd = -1

amistre64 · Answer

you essentially create 2 sets of systems of equations to solves

amistre64 · Answer

opps, i typoed myself

caozeyuan · Answer

I didn't understand your first response, although I trust you one the accuracy

amistre64 · Answer

a b   a b      -1  0
c d   c d  =   0  -1

aa + cb = -1
ac + cd = 0
ba + db = 0
bc + dd = -1

amistre64 · Answer

or we can augment A with -I, and then equate the results back to A

caozeyuan · Answer

but these equations contain 4 variables and they are all second-order, isn't too complicated?

amistre64 · Answer

its not too complicated

caozeyuan · Answer

why augment A with -I, how does that help

caozeyuan · Answer

but it's too complicated for both my self and my TI-NSpire, maybe it isn't for you genius. LOL

caozeyuan · Answer

@Loser66 , I don't know the question just said that

caozeyuan · Answer

NO here is the answer form the back of my book|dw:1373288996024:dw|