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Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is true if the columns of matrix A are a₁ = (1, -2, 0), a₂ = (-3, 4, 1), a3 = (-8, 6, 5), a4 = (-3, 0, 7) (3,3,1), Col A is a subspace of R³ O (3,1,3), Row A is a subspace of R³ O (1, 3,3), Row A is a subspace of R³ O (2,2,2), Nul A is a subspace of R¹ O (3,3,1), Col A is a subspace of R¹ O (1,3,3), Row A is a subspace of Rª (3, 1,3), Nul A is a subspace of R¹ None of the above

Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is true if the columns of matrix A are a₁ = (1, -2, 0), a₂ = (-3, 4, 1), a3 = (-8, 6, 5), a4 = (-3, 0, 7) (3,3,1), Col A is a subspace of R³ O (3,1,3), Row A is a subspace of R³ O (1, 3,3), Row A is a subspace of R³ O (2,2,2), Nul A is a subspace of R¹ O (3,3,1), Col A is a subspace of R¹ O (1,3,3), Row A is a subspace of Rª (3, 1,3), Nul A is a subspace of R¹ None of the above

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.6: Rank Of A Matrix And Systems Of Linear Equations
Problem 67E: Let A be an mn matrix where mn whose rank is r. a What is the largest value r can be? b How many...
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Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is true if the columns of matrix A are a₁ = (1, -2, 0), a₂ = (-3, 4, 1), a3 = (-8, 6, 5), a4 = (-3, 0, 7) (3,3,1), Col A is a subspace of R³ O (3,1,3), Row A is a subspace of R³ O (1, 3,3), Row A is a subspace of R³ O (2,2,2), Nul A is a subspace of Rª O (3,3,1), Col A is a subspace of R¹ O (1,3,3), Row A is a subspace of R4 O (3, 1,3), Nul A is a subspace of Rª ○ None of the above
Transcribed Image Text:Determine the triple (rank A, dim Nul A, dim Row A) and state which of the following statements is true if the columns of matrix A are a₁ = (1, -2, 0), a₂ = (-3, 4, 1), a3 = (-8, 6, 5), a4 = (-3, 0, 7) (3,3,1), Col A is a subspace of R³ O (3,1,3), Row A is a subspace of R³ O (1, 3,3), Row A is a subspace of R³ O (2,2,2), Nul A is a subspace of Rª O (3,3,1), Col A is a subspace of R¹ O (1,3,3), Row A is a subspace of R4 O (3, 1,3), Nul A is a subspace of Rª ○ None of the above
Which of the following matrices is a 2 x 2 matrix with more than one eigenvalue. [a₁ a₂], a₁ = (1, 0), a₂ = (2, 1) O [a₁ a₂], a₁ = (-2, 0), az =(4,-2) [a₁ a₂], a₁ = (3, 4), a₂ = (0,3) [a₁ a₂], a₁ = (5, 2), a2 = (0,1) all of the above None of the above
Transcribed Image Text:Which of the following matrices is a 2 x 2 matrix with more than one eigenvalue. [a₁ a₂], a₁ = (1, 0), a₂ = (2, 1) O [a₁ a₂], a₁ = (-2, 0), az =(4,-2) [a₁ a₂], a₁ = (3, 4), a₂ = (0,3) [a₁ a₂], a₁ = (5, 2), a2 = (0,1) all of the above None of the above
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