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Linear Algebra With Applications
Found in: Page 306
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

Demonstrate Theorem 6.3.6 for linearly dependent vector v1,....,vm.

Therefore, the area of the parallelepiped is given by,


See the step by step solution

Step by Step Solution

Step 1: Definition. 

Generally, the parallelepiped is a three-dimensional geometric solid with six faces that are parallelograms.

Parallelepiped is a three-dimensional solid shape.

It has 6 faces, 12 edges, and 8 vertices.

All faces of a parallelepiped are in the shape of a parallelogram.

Step 2: To demonstrate the linear dependent vectors. 

If v1,v2,.....,vm,2 are linearly dependent, then the matrix A that they form has linearly dependent columns.

Therefore, ATA is non-invertible.

So, the area of the parallelepiped is given by


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