?3.2. y, zz>0y20z>0}Determine which of the following sets are subspaces of R?1. The 3 x 3 matrices with integer entries2. The 3 x 3 matrices with trace 0.3. The 3 x 3 matrices with determinant 0tal credit on this problem??

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Answered: ? 3. {z,y,z z>0y20:20} Determine which…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section9.8: Determinants

Problem 8E

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Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many vectors are in a basis for the row space of A? c How many vectors are in a basis for the column space of A? d Which vector space Rk has the row space as a subspace? e Which vector space Rk has the column space as a subspace?
Let A and B be square matrices of order n satisfying, Ax=Bx for all x in all Rn. a Find the rank and nullity of AB. b Show that matrices A and B must be identical.
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Repeat Exercise 41 for B={(1,2,2),(1,0,0)} and x=(3,4,4). Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.

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? 3. {z,y,z z>0y20:20} Determine which of the following sets are subspaces of R ? 1. The 3 x 3 matrices with integer entries ? 2. The 3 x 3 matrices with trace 0. 2 3. The 3 x 3 matrices with determinant 0