Write a script (Program 2) to perform t he following matrix operations. Use output commands to clearly output each problem with
a problem description and result.
(a) Create the following three matrices: A = [ 9 3 5 /2 4 2/ 6 10 5 ] B = [ 1 4 4/ 0 9 4/ 2 6 1 ] C = [ 8 15 1/ 10 8 2/ 8 5 10 ]
(b) Calculate A + B and B + A to show that addition of matrices is commutative.
(c) Calculate A +( B + C ) and ( A + B )+ C to show that addition of matrices is associative.
(d) Calculate 8( A + C ) and 8A + 8C to show that multiplication by a scalar is distributive.
(e) Calculate A( B + C ) and AB + AC to show that matrix multiplication is distributive.
(f) Does AB = BA ?
(g) Find AT (transpose of A ).
(h) Calculate B-1 (inverse of B ).
(i) Calculate the product BB-1 .
(j) Create a 2x2 matrix consisting of the lower left elements of B .
(k) Create a row vector that is the vector sum of the first row of A and the third row of C .
(l) Calculate the dot product of the second row of B and the third column of C
(a) Create the following three matrices: A = [ 9 3 5 /2 4 2/ 6 10 5 ] B = [ 1 4 4/ 0 9 4/ 2 6 1 ] C = [ 8 15 1/ 10 8 2/ 8 5 10 ]
(b) Calculate A + B and B + A to show that addition of matrices is commutative.
(c) Calculate A +( B + C ) and ( A + B )+ C to show that addition of matrices is associative.
(d) Calculate 8( A + C ) and 8A + 8C to show that multiplication by a scalar is distributive.
(e) Calculate A( B + C ) and AB + AC to show that matrix multiplication is distributive.
(f) Does AB = BA ?
(g) Find AT (transpose of A ).
(h) Calculate B-1 (inverse of B ).
(i) Calculate the product BB-1 .
(j) Create a 2x2 matrix consisting of the lower left elements of B .
(k) Create a row vector that is the vector sum of the first row of A and the third row of C .
(l) Calculate the dot product of the second row of B and the third column of C
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