Question

asked 2021-01-13

Let \(A = (1, 1, 1, 0), B = (-1, 0, 1, 1,), C = (3, 2, -1, 1)\)

and let \(D = \{Q \in R^{4} | Q \perp A, Q \perp B, Q \perp C\}\).

Convince me that D is a subspace of \(R^{4}. Write D as span of a basis. Write D as a span of an orthogonal basis.

and let \(D = \{Q \in R^{4} | Q \perp A, Q \perp B, Q \perp C\}\).

Convince me that D is a subspace of \(R^{4}. Write D as span of a basis. Write D as a span of an orthogonal basis.

asked 2021-03-02

Let T be the linear transformation from R2 to R2 consisting of reflection in the y-axis. Let S be the linear transformation from R2 to R2 consisting of clockwise rotation of 30◦. (b) Find the standard matrix of T , [T ]. If you are not sure what this is, see p. 216 and more generally section 3.6 of your text. Do that before you go looking for help!

asked 2020-12-06

Use the weighted Euclidean inner product on R2 ‹u, v› = 99u1v1 + 5u2v2 where u = (u1, u2) and v = (v1, v2), to find ||w||, where w = (− 1, 3).

asked 2021-01-15

Let T denote the group of all nonsingular upper triaungular entries, i.e., the matrices of the form, [a,0,b,c] where \(\displaystyle{a},{b},{c}∈{H}\)

\(\displaystyle{H}={\left\lbrace{\left[{1},{0},{x},{1}\right]}∈{T}\right\rbrace}\) is a normal subgroup of T.

\(\displaystyle{H}={\left\lbrace{\left[{1},{0},{x},{1}\right]}∈{T}\right\rbrace}\) is a normal subgroup of T.

asked 2020-12-25

a) Let A and B be symmetric matrices of the same size.

Prove that AB is symmetric if and only \(AB=BA.\)

b) Find symmetric \(2 \cdot 2\)

matrices A and B such that \(AB=BA.\)

Prove that AB is symmetric if and only \(AB=BA.\)

b) Find symmetric \(2 \cdot 2\)

matrices A and B such that \(AB=BA.\)

asked 2020-12-15

Find the values of k for which A is not invertible. Enter all values exactly in fractional form.

A=[1,k,0,9,1,9,0,k,1]

A=[1,k,0,9,1,9,0,k,1]

asked 2020-11-24

Let n be a fixed positive integer greater thatn 1 and let a and b be positive integers. Prove that a mod n = b mon n if and only if a = b mod.

asked 2020-10-23

A single constant force F= (3i+5j) N acts ona 4.00-kg particle. (a) Calculate the work done by this forceif the particle moves from the origin to the point having the vector position r = (2i-3j) m. Does thisresult depend on the path? Explain. (b) What is the speed ofthe particle at r if its speed at the origin is 4.00 m/s? (c) What is the change in the potential energy?

asked 2021-02-23

Proove that the set of oil 2x2 matrices with entries from R and determinant +1 is a group under multiplication

asked 2021-01-25

Show that W, the set of all \(3 \times 3\) upper triangular matrices,

forms a subspace of all \(3 \times 3\) matrices.

What is the dimension of W? Find a basis for W.

forms a subspace of all \(3 \times 3\) matrices.

What is the dimension of W? Find a basis for W.