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
1 answer:
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Answer:
The fluid level difference in the manometer arm = 22.56 ft.
Explanation:
Assumption: The fluid in the manometer is incompressible, that is, its density is constant.
The fluid level difference between the two arms of the manometer gives the gage pressure of the air in the tank.
And P(gage) = ρgh
ρ = density of the manometer fluid = 60 lbm/ft³
g = acceleration due to gravity = 32.2 ft/s²
ρg = 60 × 32.2 = 1932 lbm/ft²s²
ρg = 1932 lbm/ft²s² × 1lbf.s²/32.2lbm.ft = 60 lbf/ft³
h = fluid level difference between the two arms of the manometer = ?
P(gage) = 9.4 psig = 9.4 × 144 = 1353.6 lbf/ft²
1353.6 = ρg × h = 60 lbf/ft³ × h
h = 1353.6/60 = 22.56 ft
A diagrammatic representation of this setup is presented in the attached image.
Hope this helps!
