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Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.5.44
Get Full Access to Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) - 3 Edition - Chapter 3 - Problem 3.5.44

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# find all possible values of rank(A) as a varies. a 2 13 3 22 1 aA 1 2

ISBN: 9780538735452 298

## Solution for problem 3.5.44 Chapter 3

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) | 3rd Edition

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Problem 3.5.44

find all possible values of rank(A) as a varies. a 2 13 3 22 1 aA 1 2

Step-by-Step Solution:
Step 1 of 3

Derivatives of Trig Functions:  In general, sinx)=cosx '  In general, cosx )=−sinx ' 2 1  In general, tanx )=sec x= 2 (you can derive this cos x using the trig and quotient rules)  In general, secx )=tanx∗secx (you can derive this using tri and quotient rules) The Chain Rule:  If f is differentiable at g(x)'and g is differentiable at x, then [f ∘g )x ]= f g( (x))g '(x) ' ' ' '  [(f ∘g∘h )(x)]=f g(h( x ))( h (x))h (x)  Example: x f (x)=2 f(x = ln2 Remember x 2=e 2 = (eln) =e xln2 xln2 Inner: () Outer: e (Inner)’ = ln2 () (Outer)’ = ' e ' f(x = (2x)= (exln)=e ∗ln2=e xlnln2=2 ln2 '  In general: xlna )=lna  In general: a x)=a lnaif a>0 Implicit Differentiation:  Know how to solve for y’ when it an equation is not solved for y  2 methods: o 1. You can solve the equation for y and then differentiate o 2. You can differentiate both sides of the equation and isolate y’ (called implicit differentiation). Use the chain rule to differentiate terms with y

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##### ISBN: 9780538735452

Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign) was written by and is associated to the ISBN: 9780538735452. This textbook survival guide was created for the textbook: Linear Algebra: A Modern Introduction (Available 2011 Titles Enhanced Web Assign), edition: 3. The full step-by-step solution to problem: 3.5.44 from chapter: 3 was answered by , our top Math solution expert on 01/29/18, 04:03PM. This full solution covers the following key subjects: . This expansive textbook survival guide covers 7 chapters, and 1985 solutions. Since the solution to 3.5.44 from 3 chapter was answered, more than 277 students have viewed the full step-by-step answer. The answer to “find all possible values of rank(A) as a varies. a 2 13 3 22 1 aA 1 2” is broken down into a number of easy to follow steps, and 18 words.

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