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An Introduction to linear Algebra for Science and Engineering [EXP-43742]
297 SOLVED PROBLEMS
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Question: 1.5.7
A 30 kg rail cart with a wind sail is on a frictionless track that runs northeast and southwest. A wind applies a force vector of F = [100 50] to the cart. Calculate the acceleration of the cart.
Question: 2.1.16
A boy has a jar full of coins. Altogether there are 180 nickels, dimes, and quarters. The number of dimes is one-half of the total number of nickels and quarters. The value of the coins is $16.00. How many of each kind of coin does he have?
Question: 1.1.1
An object on a frictionless surface is being pulled by two strings with force and direction as given in the diagram. (a) Represent each force as a vector in R2. (b) Represent the net force being applied to the object as a vector in R2.
Question: 1.3.1
An object that weighs 10kg is being pulled by two strings with force and direction as given in the diagram. Newton’s second law of motion says that the force F acting on the object is equal to its mass m times its acceleration a. What is the resulting acceleration of the object?
Question: 9.3.8
Are the matrices U = [1 -i i 1] and V = [1/√3(1 + i) 1/√6(1 + i) – 1/√3i 2/√6i] unitary?
Question: 2.4.7
Balance the chemical equation (NH4)3PO4 + Pb(NO3)4 → Pb3(PO4)4 + NH4NO3
Question: 2.4.6
Balance the chemical equation H3PO4 + Mg(OH)2 → Mg3(PO4)2 + H2O
Question: 9.1.11
Calculate (1 − i)(− √3 + i) and 2 + 2i / 1 + √3i using polar form.
Question: 9.1.5
Calculate (3 − 2i)(−2 + 5i).
Question: 3.1.15
Calculate [ 2 3 0 1 4 1 2 1 0 0 0 1][3 1 1 2 2 3 0 5].
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