Linear Algebra Show that if a square matrix A has two equal columns, then A is not invertible.Let A be the square matrix with columns vi v2...vn. Since two of the columns are equal, it must be that v =Vjfor some i, j. Let H be the rref(A). What can you say about leading ones in the columns i and j? What doesthat tell you about the rank of H and hence the rank of A?

since not a particular question asked ,as per guidelines solution to only first question (i.e Q1) is…

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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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Linear Algebra

Show that if a square matrix A has two equal columns, then A is not invertible.
Let A be the square matrix with columns vi v2...vn. Since two of the columns are equal, it must be that v =
Vj
for some i, j. Let H be the rref(A). What can you say about leading ones in the columns i and j? What does
that tell you about the rank of H and hence the rank of A?

Branch of mathematics concerned with mathematical structures that are closed under operations like addition and scalar multiplication. It is the study of linear combinations, vector spaces, lines and planes, and some mappings that are used to perform linear transformations. Linear algebra also includes vectors, matrices, and linear functions. It has many applications from mathematical physics to modern algebra and coding theory.

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