I'm confused on this question steps would help Let A and B two matrices of order n x n. Prove the follwoing claims:(a) N(A)nN(B) CN(A + B).(b) N(B) C N(AB)(c) R(AB) C R(A)Where N(A) represents the nullspace of A and and R(B) range of B.

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Answered: Let A and B two matrices of order n x…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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A snack company is preparing two mixtures of snacks from a supply of 110 pounds pretzels, 30 pounds pistachios, 10 pounds cheese puffs, 60 pounds sesame sticks, and 20 pounds toffee bites. Mixture X contains 55% pretzels, 20% pistachios, 5% cheese puffs, 20% sesame sticks, and no toffee bites, and sells for $7.99 per pound. Mixture Y contains 45% pretzels, 10% pistachios, no cheese puffs, 10 % sesame sticks, and 15% toffee bites, and sells for $5.99 per pound. If x = # of pounds of Snack X and y = # of pounds of Snack Y, determine the constraints on this linear programming problem. Inequality for pretzels [ Choose ] Inequality for pistachios ( Choose] Inequality for cheese puffs ( Choose ) Inequality for sesame sticks [Choose ] Inequality for toffee bits [ Choose ) Non-negativity inequalities [ Choose ] >
Please write answers in a way that is easy to follow for someone very confused . If you can’t solve all parts please solve c and d
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Let A and B two matrices of order n x n. Prove the follwoing claims: (a) N(A)NN(B) CN(A+ B). (b) N(B) C N(AB) (c) R(AB) C R(A) Where N(A) represents the nullspace of A and and R(B) range of B.