Let T: P3 → R³ be defined by T(ao+a+a₂² + 3x³) {Q.A.A} and C= Given [71 Pc (T(u)). = Pe(T(u))= = Ex: 5 3ao+a1-3a2-203 -ap + a₁-3a2 + 203 -2a0 + 3az -as Let u = 2x² + x³ B = {x³, x², x, 1}. -2 -3 1 3 4 0 0 -4 use the Fundamental Theorem of Matrix Representations to find 6 -1 -1

Q: a) Is A diagonalizable? Explain. b) If A is diagonalizable, rewrite A as XDX-1 (explain the choice…

A: a) Given            A=310010-310

Q: Prove that diagonal matrices are symmetric matrices.

A: Given: diagonal matrices are symmetric matrices

Q: Find the rank and the nullity of the matrix rank(A) = nullity(A) = rank(A) + nullity (A) = choose <…

A:

Q: upper triangular matrix is upper triangular (Use matrix transposition)

A: Here ,we have to prove that the inverse of an upper triangular matrix is upper triangular.

Q: what is a Hermitian matrix? does every Hermitian matrix has to be square matrices?

A:

Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

A:

Q: If A can be row reduced to the identity matrix, then A is not invertible. True False

A:

Q: Prove that every symmetric upper (or lower) triangular matrix is diagonal.

A: Solution: Consider the given statement " Every symmetric upper (lower) triangular matrix is…

Q: An LDU factorization of a square matrix A is a factoriza­tion A = LDU, where L is a unit lower…

A: As per the question we have to find the LDU decomposition of a matrix A And for that we will use…

Q: Each elementary matrix is invertible, and its inverse is an elementary matrix of the same type

A: Let A be a non-singular matrix of order n. Then, A can be reduced to identity matrix In by a finite…

Q: This answer is incorrect, could you please attempt it again?

A:

Q: Orthogonally diagonalizable the following matrix -4 -2) A = -4 5 2 -2 2 2

A:

Q: a) Decompose the coefficient matrix A into lower and upper triangular matrices.

A:

Q: Let A, Be M, (C) be positive definite. Prove that (4+ B)" s(A" +B").

A: Let A,B∈Mnℂ be positibve definite.  To prove A+B-1≤14A-1+B-1 Since, A and B are positive definite,…

Q: Manipulate the following matrix product to remove the parentheses ((AB)"(CDE)","

A:

Q: Proof that if matrix A is diagonalizable, then AT is diagonalizable.

A: Given that the matrix A is diagonalizable. We know that a matrix A is said to be diagonalizable if…

Q: Suppose A is invertible.  Explain AT A is invertible.

A: The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the…

Q: what is a complex matrix? Create one hermitian complex matrix ( 3 x 3)

A: The definition of a Complex matrix and a Hermitian matrix which is a type of complex matrix is…

Q: Give an example of a real square matrix that does not have an LU decomposition. Explain carefully…

A: Please see the below picture for detailed solution.

Q: If A is a square matrix such that A = A1, then A must be equal to either the identity matrix I or…

A:

Q: If b1, b2 , b3 is a basis of IR and A, B are 4 × 3 matrices satisfying Ab; = Bb; for i = 1, 2, 3…

A:

Q: One model for expenditures at high school gives the cosr C, in dollars per pupil, as a function of…

A: The quadratic equation, y=ax2+bx+c can be expressed in the vertex form as y=a(x-h)2+k, where, the…

Q: Prove [A, B] not positive and A,B are square matrices(matrix theory) [A, B] = AB - BA.

A: Given: It is given that A,B=AB-BA where, A and B are square matrices. To prove: We have to prove…

Q: (a) Hermitian, skew-hermitian, unitary and diagonal matrices are all nor- mal.

A:

Q: Define Invertible Matrices. Give an example.

A: An n x n square matrix A is called Invertible Matrices, if there exists an n x n square matrix B…

Q: find an example of a matrix in V=M3x3 that doesn't have an additive inverse ans should be entries in…

A: We have to give an example of matrix in V=M3×3 that does not have an additive inverse.

Q: Consider the elementary matrix 1 0 -- a 2 1 Describe the action of this matrix from the left in…

A: Here →A=(1,2),→B=(0,1) The vectors A, B are linearly dependent if their determinant is zero. i.e.…

Q: Write down the Invertible Matrix Theorem (yes, the whole thing!).

A:

Q: Example: Add the components of a vector (u) to the principal diagonal of a matrix (C) that is the…

A: Example of Addition of component  of vector  u to principal diagonal of a matrix C that is sum of…

Q: 4- Determining Whether a 3 x 3 Matrix A is Orthogonal or not. - A = 2 -1 2 2

A: This is a problem of linear transformation.

Q: "determine by inspection whether the matrix is invertible."

A: Method of inspection tells us that for a Triangular matrix if all the elements of the main diagonal…