SOLUTION: Let H and E be 2 × 2 matrices. Let [ 4 3 ] and [ 2 0 ] be the first and second rows of A, respectively; [ 3 6 ] and [ 2 3 ] be the first and second rows of B, respectively. If D =

Algebra ->  Matrices-and-determiminant -> SOLUTION: Let H and E be 2 × 2 matrices. Let [ 4 3 ] and [ 2 0 ] be the first and second rows of A, respectively; [ 3 6 ] and [ 2 3 ] be the first and second rows of B, respectively. If D =       Log On


   

Question 156048: Let H and E be 2 × 2 matrices. Let [ 4 3 ] and [ 2 0 ] be the first and second rows of A, respectively; [ 3 6 ] and [ 2 3 ] be the first and second rows of B, respectively. If D = H + E, then the d 11 element of D -1 is =
a. 2/9
b. 0
c. It does not exist
d. You cannot find the inverse of a matrix
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
You mention A and B but assume you mean H and E??
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H=%28matrix%282%2C2%2C4%2C3%2C2%2C0%29%29
E=%28matrix%282%2C2%2C3%2C6%2C2%2C3%29%29
D=H%2BE=%28matrix%282%2C2%2C7%2C9%2C4%2C3%29%29
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The inverse of a 2x2 matrix, A,
A=%28matrix%282%2C2%2Ca%2Cb%2Cc%2Cd%29%29
is given by
A%5E%28-1%29=DELTA%2A%28matrix%282%2C2%2Cd%2C-b%2C-c%2Ca%29%29
where
DELTA=1%2F%28ad-bc%29
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In this case,
DELTA=1%2F%287%2A3-9%2A4%29=-1%2F15
D%5E%28-1%29=DELTA%2A%28matrix%282%2C2%2C3%2C-9%2C-4%2C7%29%29
The [11] element would be %28-1%2F15%293=-1%2F5
That's not a given choice.
Please check the problem setup and re-post the question.