(a) Solve the following three equations for x1, x2, x3 in terms of b1, b2, b3. (

Question

(a) Solve the following three equations for x1, x2, x3 in terms of b1, b2, b3. (Hint: Use matrix multiplication to write-out each of the three equations.) (2 pts) [1 0 0; 1 1 0; 1 1 1] [ x1 x2 x3] = [b1 b2 b3] (x and b are column vectors; the array is 3 by 3, first row 1 0 0]

(b) The equation above can be written in “shorthand” form A x = b. Use the results of part (a) to write the solution in the form x = A1b and determine A1 . (You must show your work—you can use MATLAB only to check your answer.) (2 pts) (c) Are the columns of A dependent or independent? (circle one) (1 pt)

Explanation / Answer

Step1 : Use Matrices to solve

Step2 : use Dot product for example A = [ x1, x2,x3] in terms of B = [b1,b2,b3]

step3 : dot product is determined by AX = B

step 4 : now x1 = b1

                     -x1 + x2 = b2

                       -x2 + x3 = b3

Assume to be lower triangular

Step 6 :

Solve the system of equations using solve. The inputs to solve are a vector of equations, and a vector of variables to solve the equations for.

solve returns the solutions in a structure array. To access the solutions, index into the array

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