(2) Suppose B is a 3x3 matrix and that a) Can you tell if B is invertible? Explain ) Can tell if B is siunilor to a you, diagond matrik? If yes, Cind such diagonel matrix, If no, eyplain. why not. a

Q: Show that the matrix is not diagonalizable.

A:

Q: (3) Show that the system of quaternions can be represented as a system of real matrices of size 4 x…

A: Let h, j, k denote the imaginary units of algebra of Quaternions. Then the typical quaternion is in…

Q: Find the basis of row space of the matrix A given in the attached image . Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1, R3⇒R3+2R1, R4⇒R4-2R1,…

Q: Compute the product 0 () 0 (²) as a 2 x 2 matrix. What kind of isometry is this product?

A: Given product is  Oπ5O2π15 where Oθ represents rotation matrix through an angle θ in anti-clockwise…

Q: LARLINAD ASK YOUR TEACHER Find a basis for the nullspace of the matrix. (If ther 3 -6 8. 4 -8 -2 A =…

A:

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A:

Q: Find an LU-factorization of the matrix A such that A = LU. %3D 6 4 -2 1 -2 3 2. -2

A: Explanation of the answer is as follows

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A:

Q: Recail that two nx matrices A and B are Similer if there is an invertible matrie P Such thet p' Ap…

A:

Q: What is the coordinate matrix of that describes the following quadrilateral ABCD?

A:

Q: Is the matrix diagonalizable? If yes, find diagonal matrix D and regular matrix P such that AP = PD.…

A: Yes, Given Matrix is diagnolizable.

Q: Why is it important that the matrix is invertible? Give and example.

A:

Q: Due to what property, applied to the matrices and scalars below, do we know that (cd)A = c(dA)?

A:

Q: Let A be Sxó matrix. Knowing that Nullity (A) = 2. Then Rank(A) is equal to: * Non

A: Introduction: According to the rank-nullity theorem, Rank(A)+nullity(A)=number of columns in A Where…

Q: If the nulI snace of a 30x17 matrix is 13-dimensional, find the rank of the matrix.

A: We have been given the matrix which is of 30 x 17 i.e it has 30 rows and 17 columns. And it is also…

Q: How can I find a matrix, given the basis of the null space of said matrix?

A:

Q: Can we use cofactor expansion in a 2x2 matrix?

A: Can we use cofactor expansion in a 2x2 matrix?

Q: A diagonal matrix is a square matrix that if rotated to give the original matrix 1- right 2-Error

A: a diagonal matrix is a matrix in which the entries outside the main diagonal are all zero; the term…

Q: Is the matrix A = [] diagmalızable? Exploin %3D

A:

Q: • Is it possible for a 5 x 5 matrix to be invertible when its columns do not span R°? Why or why…

A: According to the Invertible matrix theorem, the matrix with n x n order cannot be invertible if its…

Q: Explain why the row vectors of a 8 × 7 matrix form a linearly dependent set. (Assume all matrix…

A: Consider the given information. The given matrix in the form of 8 *7 matrix, forms a linearly…

Q: If there is conformability what are the dimensions of the product matrix?

A: let's matrix A and matrix B has dimension as  m×n and n×p respectively then dimension of matrix…

Q: Find the rank and nullity of the matrix; then verify that the values obtained satisfy Formula 4 of…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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A: It is given that the matrix A satisfies the equation A-1=AT and we know that this condition is…

Q: Show that the matrix below does not have an LU-factorization.

A:

Q: Explain why the row vectors of a 7 x 2 matrix form a linearly dependent set. (Assume all matrix…

A: Rank of the matrix is at most min(7,2) = 2 dimension of row space = rank of matrix

Q: A 3x4 matrix A has Rank 1, then dim NUTLA %3D

A: The rank nullity theorem says that if T is a linear transformation form a vector Space V to vector…

Q: Due to what property, applied to the matrices and scalars below, do we know that c(A + B) = cA + cB…

A: Given: We have to state which property for c(A + B) = cA + cB and (c + d)A = cA + dA

Q: A matrix that is both upper and lower. triangular is called diagonal ylgn ihi

A: Upper and lower triagular matrix

Q: Is the sum of two invertible matrices invertible? Explain why or why not. Illustrate your conclusion…

A:

Q: a The fallowing A ond B!, matrices goveric 3* madrices are How wouldyou OL express, the Sum a the…

A: Given matrix is, A=a11a12a13a21a22a23a31a32a33B=b11b12b13b21b22b23b31b32b33

Q: A real square matrix Q is called orthogonal if QTQ = I. Prove det(Q) = ±1. Give an example of such a…

A: Solution

Q: Suppose AB = C, where A and C are upper triangular. (a) Find 2 × 2 nonzero matrices A, B, C, where B…

A: Answer

Q: 6. What 2x 2 matrix rotates the plane clockwise by 90° while dilating it by a factor of 2?

A: We need to find such a 2×2 matrix which rotates the plane clockwise by 90° while dilating it by a…

Q: what is the determinant of an upper/lower triangular matrix?

A: This question is related to Linear Algebra. Here the determinant of upper/lower triangular matrix is…

Q: If the null space of a 7 x 6 matrix A is 5-dimensional, what is the dimension of the column space of…

A: We solve given problem with the help of rank nullity theorem

Q: Can arrowhead matrix be similar to a tridiagonal matrix?

A: An arrowhead matrix is one that is a square matrix with zero entries everywhere except on the…

Q: If A is a square matrix whose rows add up to the zero vector, explain why A cannot be invertible.

A: Given A is square matrix whos rows add up to zero vector.

Q: Show that a triangular matrix is normal if it is diagonal

A: Given: A triangular matrix is normal.if it is diagonal

Q: Show that for itermitian matrix C any S hew that

A: To prove: ρ(C) = C2

Q: Suppose A, C are square invertible matrices, and B is a matrix of such size that the block matrix вс…

A: Given A and C are square invertible matrices. Further given that B is a matrix of such size that the…

Q: How do the dimensions of the null space and column space of a matrix relate to the number of lead…

A:

Q: Show that (-A) T= -A", where A is a 2x3 type matrix (you can show it on the example)

A: Let matrix A=abcdef. Order of matrix A is 2×3. ⇒-A=-a-b-c-d-e-f ⇒(-A)T=-a-d-b-e-c-f  →Result 1

Q: Explain why the row vectors of a 9 x 6 matrix form a linearly dependent set. (Assume all matrix…

A:

Q: - Suppose that A and B arenxn matrices and A is invertible. Invent and prove a theorem that…

A: Solution

Q: Find the basis of column space of the matrix A given in the attached image .Please answer quickly .

A: A=1231337638-2-5-30326024351312R2⇒R2-3R1,…

Q: a) In statistical theory, a common requirement is that a matrix be of full rank. That is, the rank…

A: Hello. Since your question has multiple parts, we will solve the first part for you. If you want…