Use the fact that matrices A and 8 are row-equivalent.-2-5-5-3 -517 -13 5100 1 -2 0 3o o O 1 -so O O o7 5-43-310Ca) Find the rank and nulity of A.ranknullity(b) Find a basls for the nullspace of A.(C) Find a basis for the row space of A.(0 Find a bk for the colume space of AW Determine nhethe or net the ows of A w ineaty ndoperdent.O ndependertO dependertO ia, a a

Given matrix A is equivalent to matrix B so rank and nullity also same matrix A and matrix B

Answered: -2-5 BO-17 -5 1 A- -3-5 75-43 1 7 -13 S…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CM: Cumulative Review

Problem 8CM: Take this test to review the material in Chapters 4 and 5. After you are finished, check your work...

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Similar questions

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.
Find an orthogonal matrix P such that PTAP diagonalizes the symmetric matrix A=[1331].
A square matrix A=[aij]n with aij=0 for all ij is called upper triangular. Prove or disprove each of the following statements. The set of all upper triangular matrices is closed with respect to matrix addition in Mn(). The set of all upper triangular matrices is closed with respect to matrix multiplication in Mn(). If A and B are square and the product AB is upper triangular, then at least one of A or B is upper triangular.
12. Positive integral powers of a square matrix are defined by and for every positive integer. Evaluate and and compare the results for and.
Let A,D, and P be nn matrices satisfying AP=PD. Assume that P is nonsingular and solve this for A. Must it be true that A=D?
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.
A square matrix is called upper triangular if all of the entries below the main diagonal are zero. Thus, the form of an upper triangular matrix is where the entries marked * are arbitrary. A more formal definition of such a matrix . 29. Prove that the product of two upper triangular matrices is upper triangular.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Determine whether the columns of matrix A span R4. A=[1210130200111001]

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-2-5 BO-17 -5 1 A- -3-5 75-43 1 7 -13 S -3 01 -2 0 3 o o o 1-S Ca) Find the rank and nullity of A. rank nullity (b) Find a basis for the nullspace of A. (C) Find a basis for the row space of A. 10 Fnd colune space of A. a bas for the ary independent