Didn’t find what you are looking for?

Matrix transformations

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

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

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

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

Matrix transformations

(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

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

Write an augumented matrix for the system of linear equations $$[[x-y+z=8],[y-12z=-15],[z=1]]$$

Matrix transformations

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

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

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

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

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

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

Solve the following pair of linear equations by the elimination method and the substitution method: x + y = 5, 2x - 3y = 4

Matrix transformations

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