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Matrix transformations Answers
Matrix transformations
asked 2021-03-07
Give the elementary matrix that converts
[-2,-2,-1,-3,-1,-3,1,-4,-3] to [-6,-2,-1,-5,-1,-3,-7,-4,-3]
Matrix transformations
asked 2021-03-04
Show that
\(\displaystyle{C}^{\ast}={R}^{\ast}+\times{T},\text{where}\ {C}^{\ast}\)
is the multiplicative group of non-zero complex numbers, T is the group of complex numbers of modulus equal to 1,
\(\displaystyle{R}^{\ast}+\)
is the multiplicative group of positive real numbers.
Matrix transformations
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!
Matrix transformations
asked 2021-02-23
Proove that the set of oil 2x2 matrices with entries from R and determinant +1 is a group under multiplication
Matrix transformations
asked 2021-02-21
(7) If A and B are a square matrix of the same order. Prove that
\(\displaystyle{\left({A}{B}{A}^{
Matrix transformations
asked 2021-02-14
If A =[1,2,4,3], find B such that A+B=0
Matrix transformations
asked 2021-02-12
Write the given matrix equation as a system of linear equations without matrices.
\([(2,0,-1),(0,3,0),(1,1,0)][(x),(y),(z)]=[(6),(9),(5)]\)
Matrix transformations
asked 2021-02-11
Let A be a 6 X 9 matrix. If Nullity
\(\displaystyle{\left({A}{T}{A}^{{T}}{A}{T}\right)}\)
= 2 then Nullity(A) = 2
Matrix transformations
asked 2021-02-08
Write an augumented matrix for the system of linear equations
\([[x-y+z=8],[y-12z=-15],[z=1]]\)
Matrix transformations
asked 2021-02-06
1:Find the determinant of the following mattrix
\([((2,-1,-6)),((-3,0,5)),((4,3,0))]\)
2: If told that matrix A is singular Matrix find the possible value(s) for x
\(A = { (16x, 4x),(x,9):}\)
Matrix transformations
asked 2021-01-25
Let D be the diagonal subset
\(\displaystyle{D}={\left\lbrace{\left({x},{x}\right)}{\mid}{x}∈{S}_{{3}}\right\rbrace}\)
of the direct product S_3 × S_3. Prove that D is a subgroup of S_3 × S_3 but not a normal subgroup.
Matrix transformations
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.
Matrix transformations
asked 2021-01-24
It can be shown that the algebraic multiplicity of an eigenvalue lambda is always greater than or equal to the dimension of the eigenspace corresponding to lambda. Find h in the matrix A below such that the eigenspace for lambda = 5 is two-dimensional:
\(\displaystyle{A}={\left[\begin{array}{cccc} {5}&-{2}&{6}&-{1}\\{0}&{3}&{h}&{0}\\{0}&{0}&{5}&{4}\\{0}&{0}&{0}&{1}\end{array}\right]}\)
Matrix transformations
asked 2021-01-23
Find basis and dimension
\(\displaystyle{\left\lbrace{x}{e}{R}^{{4}}{\mid}{x}{A}={0}\right\rbrace}\)
where
\(\displaystyle{A}={\left[-{1},{1},{2},{1},{1},{0},{2},{3}\right]}^{{T}}\)
Matrix transformations
asked 2021-01-22
Let
\(\displaystyle{u}={i}+{2}{j}-{3}{k}\)
and
\(\displaystyle{v}={2}{i}+{3}{j}+{k}\in{R}^{{3}}\)
(a) What is u * v?
(b) What is u * v?
Matrix transformations
asked 2021-01-19
Solve the following pair of linear equations by the elimination method and the substitution method:
x + y = 5, 2x - 3y = 4
Matrix transformations
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.
Matrix transformations
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.
Matrix transformations
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
\(AB=BA.\)
Matrix transformations
asked 2020-12-21
Check
\((2 1,0 0),(0 0,2 0),(3 -1,0 0),(0 3, 0 1)\)
is a bais for M22 or not?
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