Will y’all help me on 16 thank you
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where det(<em>A</em>) = 1×1 - 2×1 = -1.
where det(<em>B</em>) = 0×2 - (-1)×1 = 1. Then
On the other side, we have
and det(<em>AB</em>) = det(<em>A</em>) det(<em>B</em>) = (-1)×1 = -1. So
and both matrices are clearly the same.
More generally, we have by definition of inverse,
where is the identity matrix. Multiply on the left by <em>A </em>⁻¹ to get
Multiplication of matrices is associative, so we can regroup terms as
Now multiply again on the left by <em>B</em> ⁻¹ and do the same thing:
Let be the number of hours worked at Job A and
the number of hours at Job B. Then
and
From the first equation,
and substituting this into the second gives