Determine the rank and nullity of the matrix.2 -1 0 15 21 -4-1 -4 -1 6-8 -5 -2 9The rank of the matrix isThe nullity of the matrix is

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Answered: Determine the rank and nullity of the…

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Matrices And Determinants

Section7.3: The Inverse Of A Square Matrix

Problem 1E

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Find ATA and AAT for the matrix below. What do you observe? A=[132461]
(a) The matrix I=[1001] is called an _____ matrix. (b) If A is a 22 matrix, then AI= _____ and IA= _____. (c) If A and B are 22 matrices with AB=I , then B is the _____ of A.
Fill in the blanks. If A is an invertible matrix, then the system of linear equations represented by AX=B has a unique solution given by X=.
Guided Proof Prove that if A is row-equivalent to B, and B is row-equivalent to C, A is row-equivalent to C. Getting Started: to prove that If A is row-equivalent to C, you have to find elementary matrices E1, E2. Ek such that A=EkE2E1C. i Begin by observing that A is row-equivalent to B and B is row-equivalent to C. ii This means that there exist elementary matrices F1F2Fn and G1G2Gm such that A=FnF2F1B and B=GmG2G1C. iii Combine the matrix equations from step ii.
CAPSTONE In the matrix equation aX+AbB=bAB+IB X,A,B and I are square matrices, and a and b are non-zero scalars. Justify each step in the solution below. aX+AbB=bAB+B aX+bAB=bAB+bB aX+bAB+-bAB=bAB+bB+-bAB aX=bAB+bB+-bAB aX=bAB+-bAB+bB aX=bB X=baB
Nutrition Refer to Exercise 61. Suppose food type C has been improperly labeled, and it actually contains 4 mg of folic acid, 6 mg of choline, and 5 mg of inositol per ounce. Would it still be possible to use matrix inversion to solve parts (b), (c), and (d) of Exercise 61? Why or why not?

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Determine the rank and nullity of the matrix. 2 -1 0 1 5 2 1 -4 -1 -4 -1 6 -8 -5 -2 9 The rank of the matrix is The nullity of the matrix is