If A = 1 2 1 1 and B= 0 -1 1 2 then show that (AB)^-1 = B^-1 A^-1

help m ple ​

where det(A) = 1×1 - 2×1 = -1.

where det(B) = 0×2 - (-1)×1 = 1. Then

On the other side, we have

and det(AB) = det(A) det(B) = (-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 A ⁻¹ to get

Multiplication of matrices is associative, so we can regroup terms as

Now multiply again on the left by B ⁻¹ and do the same thing:

d. 24+-0.114

step-by-step explanation:

the question requires us to calculate the approximate 95% confidence interval for the mean number of ounces of ketchup per bottle in the sample given the following statistics;

sample mean = 24

standard deviation, σ = 0.4

sample size , n = 49

the confidence interval for a population mean is calculated using the formula;

sample mean ± z-score*(σ/sqrt(n))

the z-score associated with a 95% confidence interval, from the standard normal tables, is;

1.96

substituting these values into the formula;

24 ± 1.96*(0.4/7)

= 24 ± 0.112

from the alternatives given, choice d is closest to the above expression;