Construct two normal matrices A, B € M4, that are neither Hermitian or i times a Hermitian, by letting Re A = Re B be the matrix where every entry is 1 and finding nonzero Im A + Im B that commute with the Re A = Re B.

Q: Explain why the columns of an nxn matrix A are linearly independent when A is invertible.

A: The objective of this question is to understand the relationship between the invertibility of a…

Q: If the matrix A is positive symmetric definite, is BTAB also positive symmetric definite?

A: Let us define the function as, A¯=BTAB Then, A¯T=BTABT=BATBT=BABT   [A is symmetric]

Q: Let A and B be n x n matrices. Their product, AB, is singular. Show at least one of A or B must be…

A: Let A and B be n×n matrices such that their product AB is singular.We have to show that at least one…

Q: Let A and B be two square matrices of the same size. Prove that det(AB) = det(BA).

A: Using Determinant and elementary row operations,

Q: and the SUD of the following am A= 11 94040 220

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Q: y = - 1.5 cos (3x -90) +0.5   what is the    a) period  b) amplitude  c) the phase shift

A: Since you have uploaded multiple part questions according to our guidelines we have solved the first…

Q: Suppose that A and B are invertible 2 x 2 matrices such that det(AT) = 2 and det(B) = -2. Let x ER…

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Q: Find an orthogonal diagonalization for A = 1 0 1 0 1 -1 (1888) -1 1 i.e. find an orthogonal matrix U…

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Q: Let A be a symmetric positive definite n×n matrix and let S be a nonsingular n × n matrix. Show that…

A: To show that STAS is positive definite, we need to prove two things: 1. STAS is symmetric. 2. For…

Q: Determine the Householder matrix that annihilates all but the first entry of the vector v = [2 22…

A: Let α=2222T Then take, v=α-αc1=2222-α2000=2222-α000 ,Here α=±||a||2=±2 Now , since,α1  is positive ,…

Q: Seven thieves try to share a hoard of gold bars equally between themselves. Unfortunately, six bars…

A: Seven thieves try to share a hoard of gold bars equally between themselves.Unfortunately, six bars…

Q: Let A and C be n×n matrices such that ​CA=I​ (the n×n identity​ matrix). Show that Ax​=0 has only…

A: Here, CA=I, where I is the identity matrix.

Q: Let A be an m x n matrix and let b and c be column vectors with n components. Express the dot…

A: Answer :

Q: Construct a 4×3 matrix A and vectors ~b and ~c in R4 so that ~b is in the range ofthe linear…

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Q: Let A be a 2 × 2 real matrix. Determine conditions on the entries of A so that A2 = I2.

A: Given: Let A be a 2 x 2 real matrix.   To determine: The conditions on the entries of A so that A2 =…