Which of the following is true?Select all possible answers.|If we square an arbitrary matrix A the eigenvalue of A? can be computed from the eigenvalue of AThe eigenvalues of an upper triangular matrix are its diagonal entriesFor any two matrices A and B the eigenvalues of Aand Bare always the sum of the eigenvalues of Aand BOIf U and V are two vector spaces, then the basis of their union is the union of the basis sets of U and V Let, Aand Bbe two 10 x 10matrices. What can we say about the null space of A x BThe null space of A x Bs always a subspace of the null space of BThe null space of Bis always a subspace of the null space of A x BThe null space of Ais always a subspace of the null space of A x BThe null space of A x Bs always a subspace of the null space of A

In first,option first, fourth and second is true. In second, option 2nd &3rd is true.

Answered: Let, Aand Bbe two 10 x 10matrices. What…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.3: Subspaces Of Vector Spaces

Problem 13E: Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by...

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Similar questions

Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}
Give an example showing that the union of two subspaces of a vector space V is not necessarily a subspace of V.
Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x+y=xyAddition cx=xcScalar multiplication If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
Let V be an two dimensional subspace of R4 spanned by (0,1,0,1) and (0,2,0,0). Write the vector u=(1,1,1,1) in the form u=v+w, where v is in V and w is orthogonal to every vector in V.
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. Prove that the set of all singular 33 matrices is not a vector space.
Let B={(0,2,2),(1,0,2)} be a basis for a subspace of R3, and consider x=(1,4,2), a vector in the subspace. a Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B. b Apply the Gram-Schmidt orthonormalization process to transform B into an orthonormal set B. c Write x as a linear combination of the vectors in B.That is, find the coordinates of x relative to B.
Consider the vector spaces P0,P1,P2,...,Pn where Pk is the set of all polynomials of degree less than or equal to k, with standard operations. Show that if jk, then Pj is the subspace of Pk.
Subsets That Are Not Subspaces In Exercises 7-20 W is not a subspace of vector space. Verify this by giving a specific example that violates the test for a vector subspace Theorem 4.5. W is the set of all vectors in R3 whose components are nonnegative.

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