Amatrix is skew symmetric of a^t = -a. prove that if b is a square matrix that 1/2(b - b^t) is skew symmetric and 1/2(b + b^t) is symmetric. find the inverse of a = [1 2 0 2 1 0 0 0 3] if it exists. a) give a 2 times 2 example that proves that the sum of two invertible matrices need not be invertible. b) give a 2 times 2 example that proves that the sum of two singular matrices need not be singular. let a be an invertible matrix. prove that if ab is defined then rank ab = rank b and if ba is defined that rank ba = rank b.

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation: