Consider the 2x3 matrix A = 1 0 4 0 2 1over the field Q of rationals.Using elementary row and column operations, or otherwise, find invertible matrices P, Q such that the matrix PAQ is in canonical form for equivalenceLet A be an n × n matrix with a column of zeros. Show directly from the Leibniz formula for determinants that det(A) = 0.Now suppose that V has a basis v1, v2, v3 and W a basis w1, w2, and letα : V → W be the linear map corresponding to the matrix A in (b) with respectto these bases. State the values α(v1), α(v2), α(v2). What is the rank ρ(α)?

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Answered: Consider the 2x3 matrix A = 1 0 4…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Consider the 2x3 matrix A = 1 0 4

0 2 1

over the field Q of rationals.

Using elementary row and column operations, or otherwise, find invertible matrices P, Q such that the matrix PAQ is in canonical form for equivalence
Let A be an n × n matrix with a column of zeros. Show directly from the Leibniz formula for determinants that det(A) = 0.
Now suppose that V has a basis v1, v2, v3 and W a basis w1, w2, and let
α : V → W be the linear map corresponding to the matrix A in (b) with respect
to these bases. State the values α(v1), α(v2), α(v2). What is the rank ρ(α)?

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