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Start with 100 equations Ax= 0 for 100 unknowns x = (x1, ... ,x100). Suppose elimination reduces the 100th equation to O = 0, so the system is "singular".(a) Elimination takes linear combinations of the rows. So this singular system has the singular property: Some linear combination of the 100 rows is ___.(b) Singular systems Ax = 0 have infinitely many solutions. This means that some linear combination of the 100 columns is(c) Invent a 100 by 100 singular matrix with no zero entries.(d) For your matrix, describe in words the row picture and the column picture of Ax = 0. Not necessary to draw 100-dimensional space.

Start with 100 equations Ax= 0 for 100 unknowns x = (x1, ... ,x100). Suppose elimination reduces the 100th equation to O = 0, so the system is "singular".(a) Elimination takes linear combinations of the rows. So this singular system has the singular property: Some linear combination of the 100 rows is ___.(b) Singular systems Ax = 0 have infinitely many solutions. This means that some linear combination of the 100 columns is(c) Invent a 100 by 100 singular matrix with no zero entries.(d) For your matrix, describe in words the row picture and the column picture of Ax = 0. Not necessary to draw 100-dimensional space.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 15EQ
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Start with 100 equations Ax= 0 for 100 unknowns x = (x1, ... ,x100). Suppose elimination reduces the 100th equation to O = 0, so the system is "singular".
(a) Elimination takes linear combinations of the rows. So this singular system has the singular property: Some linear combination of the 100 rows is ___.
(b) Singular systems Ax = 0 have infinitely many solutions. This means that some linear combination of the 100 columns is
(c) Invent a 100 by 100 singular matrix with no zero entries.
(d) For your matrix, describe in words the row picture and the column picture of Ax = 0. Not necessary to draw 100-dimensional space.

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