If the column space of a 3x3 matrix consists of all vectors b=[b1 b2 b3] such that b1+ b2= 3b3 then one of the following set of the vectors forms abasis for the left null space of that matrix: O[11 - 31] O[113] and [11 -3] O [33-1] O [33 1] and [3 3 - 1]

If the column space of a 3x3 matrix consists of all vectors b=[b1 b2 b3] such that b1+ b2= 3b3 then one of the following set of the vectors forms abasis for the left null space of that matrix: O[11 - 31] O[113] and [11 -3] O [33-1] O [33 1] and [3 3 - 1]

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

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

If the column space of a 3x3 matrix consists of all vectors b=[b¡ b2 b3] such that b1+ b2= 3b3 then
one of the following set of the vectors forms abasis for the left null space of that matrix:
O [ 11 - 3]
O[113] and [11 -3]
O[33-1]
O[33 1] and [3 3 - 1]

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