20. Let A = (a;j) be a given (3 × 3) matrix. Form the associated (3 x 5) matrix B shown next: a12 B = | a21 a22 a) Subtract the sum of the three upward diagonal products from the sum of the three downward diagonal products and argue that your result is equal to det(A). b) Show, by example, that a similar basketweave algorithm cannot be used to calculate the determinant of a (4 × 4) matrix.

20. Let A = (a;j) be a given (3 × 3) matrix. Form the associated (3 x 5) matrix B shown next: a12 B = | a21 a22 a) Subtract the sum of the three upward diagonal products from the sum of the three downward diagonal products and argue that your result is equal to det(A). b) Show, by example, that a similar basketweave algorithm cannot be used to calculate the determinant of a (4 × 4) matrix.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.2: Direct Methods For Solving Linear Systems

Problem 22EQ: Consider the matrix A=[2314]. Show that any of the three types of elementary row operations can be...

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