Question

In: Advanced Math

Let H be the subset of all skew-symmetric matrices in M3x3 a.) prove that H is...

Let H be the subset of all skew-symmetric matrices in M3x3

a.) prove that H is a subspace of M3x3 by checking all three conditions in the definition of subspace.

b.) Find a basis for H. Prove that your basis is actually a basis for H by showing it is both linearly independent and spans H.

c.) what is the dim(H)

Solutions

Expert Solution


Related Solutions

Let A be an infinite set and let B ⊆ A be a subset. Prove: (a)...
Let A be an infinite set and let B ⊆ A be a subset. Prove: (a) Assume A has a denumerable subset, show that A is equivalent to a proper subset of A. (b) Show that if A is denumerable and B is infinite then B is equivalent to A.
b) a matrix is skew symmetric if AT=-A.If A is a skew-symmetric matrix of odd order,show...
b) a matrix is skew symmetric if AT=-A.If A is a skew-symmetric matrix of odd order,show that A is not invertible c)Let A and B be n*n matrixes with detA=detB not equal to 0,If a and b are non zero real numbers show that det (aA+bB-1)=det(aB+bA-1)
Abstract Algebra For the group S4, let H be the subset of all permutations that fix...
Abstract Algebra For the group S4, let H be the subset of all permutations that fix the element 4. a) show this is a subgroup b) describe an isomorphism from S3 to H
1. Let A be an inductive subset of R. Prove that {1} ∪ {x + 1...
1. Let A be an inductive subset of R. Prove that {1} ∪ {x + 1 | x ∈ A} is inductive. 2. (a) Let n ∈ N(Natural number) and suppose that k 2 < n < (k + 1)2 for some k ∈ N. Prove that n does not have a square root in N. (b) Let c ∈ R \ {0}. Prove that if c has a square root in Z, then c has a square root in...
Let G, H, K be groups. Prove that if G ≅ H and H ≅ K...
Let G, H, K be groups. Prove that if G ≅ H and H ≅ K then G ≅ K.
hzhshs assume that X is normed linear space let A is a subset of X prove...
hzhshs assume that X is normed linear space let A is a subset of X prove that: if A is compact then A is closed and bounded
Let X be a subset of R^n. Prove that the following are equivalent: 1) X is...
Let X be a subset of R^n. Prove that the following are equivalent: 1) X is open in R^n with the Euclidean metric d(x,y) = sqrt((x1 - y1)^2+(x2 - y2)^2+...+(xn - yn)^2) 2) X is open in R^n with the taxicab metric d(x,y)= |x1 - y1|+|x2 - y2|+...+|xn - yn| 3) X is open in R^n with the square metric d(x,y)= max{|x1 - y1|,|x2 - y2|,...,|xn -y n|} (This can be proved by showing the 1 implies 2 implies 3)...
Show that the set of all n × n real symmetric matrices with zero diagonal entries...
Show that the set of all n × n real symmetric matrices with zero diagonal entries is a subspace of Rn×n
Incorrect Theorem. Let H be a finite set of n horses. Suppose that, for every subset...
Incorrect Theorem. Let H be a finite set of n horses. Suppose that, for every subset S ⊂ H with |S| < n, the horses in S are all the same color. Then every horse in H is the same color. i) Prove the theorem assuming n ≥ 3. ii) Why aren’t all horses the same color? That is, why doesn’t your proof work for n = 2?
Let x ∈ Rn be any nonzero vector. Let W ⊂ Rnxn consist of all matrices...
Let x ∈ Rn be any nonzero vector. Let W ⊂ Rnxn consist of all matrices A such that Ax = 0. Show that W is a subspace and find its dimension.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT