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Linear Algebra With Applications
Found in: Page 400
Linear Algebra With Applications

Linear Algebra With Applications

Book edition 5th
Author(s) Otto Bretscher
Pages 442 pages
ISBN 9780321796974

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Short Answer

Consider a quadratic form


where A is a symmetric nxn matrix. Find q(e1). Give your answer in terms of the entries of the matrix A.


See the step by step solution

Step by Step Solution

Step 1: Given Information:


Step 2: Determining :

Take a look at the quadratic form:


Where A is a nxn symmetric matrix Take into account this:

A=aij where 1i,jn

Now, use the following formula to access qe1:

localid="1659613659189" qe1=e1.Ae1 =e1j-1naj1ej =j-1naj1ei.ej qe1=a11 Since e1.ej=δij

Step 3: Determining the Result:


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