Let Eequals={Bold e 1e1, Bold e 2e2, Bold e 3e3} be the standard basis for set of real numbers Rℝ3, Bequals={Bold b 1b1, Bold b 2b2, Bold b 3b3} be a basis for a vector space V, and T : set of real numbers Rℝ3 right arrow→ V be a linear transformation with the property that Upper T (x 1 comma x 2 comma x 3 )Tx1, x2, x3equals=(x 2 minus x 3 )x2−x3Bold b 1b1plus (x 1 plus x 3 )+x1+x3Bold b 2b2plus (x 2 minus x 1 )+x2−x1Bold b 3b3.

a. Find the change-of-coordinates matrix from Upper B to Upper A.
b. Find left bracket Bold x right bracket Subscript Upper A for Bold x equals Bold b 1 minus 4 Bold b 2 plus 4 Bold b 3.

Prove that 3: 8 is equivalent to 12: 32.a. use diagrams to support your answer.

The rate of decay of a radioactive substance depends upon the amount present initially. the mass y (mg) of the radioactive substance cobalt-60 present in a sample at time t (years) is represented by the exponential equation y=50e −0.1315 t . answer the following questions in complete sentences. 1. how does the exponential equation above compare to the equation for simple interest that is compounded continuously? explain the similarities. 2. what is the initial amount of cobalt-60 in the sample? 2. how much cobalt-60 is left after 8.4 years? show your work. 3. what would be the y-intercept of the graph? what does it represent? 4. after how many years will the amount of cobalt-60 left be 6.25 mg? explain what happens to the cobalt-60 after 50 years? 5. discuss some “real-world” examples and uses of cobalt-60

Ineed someone to me answer my question i have to have this done and knocked out