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1. True or False: a). b) Every basis of R³ has 2 vectors The standard basis of P4, polynomials of degree less than or equal to 4, is {1,1, x², x³, x4¹} c). The matrix equation Ax = b is consistent if and only if b is in the col(A), the column space of A The set {x d) e) - If T: V→ spaces V, W then f). h) R² : 2+2 ≤ 1} is a vector subspace of R² W is a linear transformation between finite dimensional vector dim(V) = dim(N(T)) + dim(R(T)) A linear transformation is one to one if its nullspace contains 6 nonzero vectors. Every n x n symmetric matrix is orthogonally diagonalizable. An eigenvector is always nonzero.

1. True or False: a). b) Every basis of R³ has 2 vectors The standard basis of P4, polynomials of degree less than or equal to 4, is {1,1, x², x³, x4¹} c). The matrix equation Ax = b is consistent if and only if b is in the col(A), the column space of A The set {x d) e) - If T: V→ spaces V, W then f). h) R² : 2+2 ≤ 1} is a vector subspace of R² W is a linear transformation between finite dimensional vector dim(V) = dim(N(T)) + dim(R(T)) A linear transformation is one to one if its nullspace contains 6 nonzero vectors. Every n x n symmetric matrix is orthogonally diagonalizable. An eigenvector is always nonzero.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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1. True or False: a) Every basis of R³ has 2 vectors b) The standard basis of P4, polynomials of degree less than or equal to 4, is {1, x, x², x³, x4} c) The matrix equation Ax=b is consistent if and only if b is in the col(A), the column space of A d) e) - f) h) - The set {x € R² : 2+2 ≤ 1} is a vector subspace of R² - If T V I spaces V, W then W is a linear transformation between finite dimensional vector dim(V)= dim(N(T)) + dim(R(T)) A linear transformation is one to one if its nullspace contains 6 nonzero vectors. Every n x n symmetric matrix is orthogonally diagonalizable. An eigenvector is always nonzero.
Transcribed Image Text:1. True or False: a) Every basis of R³ has 2 vectors b) The standard basis of P4, polynomials of degree less than or equal to 4, is {1, x, x², x³, x4} c) The matrix equation Ax=b is consistent if and only if b is in the col(A), the column space of A d) e) - f) h) - The set {x € R² : 2+2 ≤ 1} is a vector subspace of R² - If T V I spaces V, W then W is a linear transformation between finite dimensional vector dim(V)= dim(N(T)) + dim(R(T)) A linear transformation is one to one if its nullspace contains 6 nonzero vectors. Every n x n symmetric matrix is orthogonally diagonalizable. An eigenvector is always nonzero.
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