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New PDF release: Calculus and Linear Algebra. Volume 2: Vector Spaces,

By Wilfred Kaplan, Donald J. Lewis

ISBN-10: 0471456888

ISBN-13: 9780471456889

ISBN-10: 1425589340

ISBN-13: 9781425589349

ISBN-10: 1425589359

ISBN-13: 9781425589356

Within the moment quantity of Calculus and Linear Algebra, the concept that of linear algebra is extra constructed and utilized to geometry, many-variable calculus, and differential equations.

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Extra resources for Calculus and Linear Algebra. Volume 2: Vector Spaces, Many-Variable Calculus, and Differential Equations

Sample text

Z) = (- I. 2. 2). 'The row picture has th= planes from three equations. All the planes go through this solution. The original planes are sloping. t plane 4: = 8 after elimination is horizontal. "The column picture shows a combination of column ,'ectors producing the righl side h . y. Z multiply columns I. 2. 3 in the original system Ax "", b and also in the triangular system Ux '" c. fVr a 4 by 4 problem. or an n by n problem. >ds lhe same " ·a)". Here is the whole idea of forward elimination. column by column: Column 1.

So that a ;} is an enll)' in row i . The sewnd index j gi,'cs the col umn number. But those subscri pts are not convcnient on a keyboard! ln Slcad of oi) it is easier to type A(I . j). , O~J = A(5. 7) ""Quid 1M in ro ... 5, colum" 7. A. [all OIl]. 2) . r-or an nI by n matri~. lhe row index i goes from 110m. TIle column index j stops at n. ~. A squart: matrix (order,, ) 1Ias,,2 enlrics. Mulliplication in MATlAB I want to express A and x and their product Ax using MATlAB commands. This is a first step in learning that language.

Matrix addition is easy. The serious qucstion is mmnx mllu,'p/icolion. When can we multiply A times B. and what is the prodllCt AB? We canOOl multiply " 'hen A and B are 3 by 2. s. If A has LwO columns. B mu'\L ha>-e two rows. When A i~ 3 by 2. the matrix tJ un be 2 by I (a "«Lor) or 2 by 2 (square) or 2 by 20. E>-ery column of B is ready to be multiplied by A. Tkn A B i! 3 by I (a >-eclor) or 3 by 2 or 3 by 20.

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Calculus and Linear Algebra. Volume 2: Vector Spaces, Many-Variable Calculus, and Differential Equations by Wilfred Kaplan, Donald J. Lewis


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