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
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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