Find a basis for the null space of the matrix given below.11-4-1 100 1-3 -30 0 -70 21A basis for the null space is {}(Use a comma to separate answers as needed.)t tdart(MatHelp me solve thisView an exampleGet more help-

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Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 48CR: Find an orthonormal basis for the solution space of the homogeneous system of linear equations....

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Find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].
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a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving that if A is an nn symmetric matrix with positive eigenvalues, then there exists a symmetric matrix B such that B2=A.

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Find a basis for the null space of the matrix given below. 11-4 -1 10 0 1 0 -3 -3 0 0-7 021 A basis for the null space is {} (Use a comma to separate answers as needed.)