#### 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 ### 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.$$ 