4. Let A € Rnxn, u, v € Rn. Compute the inverse of A = 1 + uv¹. Hint: try a matrix I-auvT with a R to be determined. What constraint must u and v satisfy for the inverse to exist?

Q: 2. Let A be a square matrix with real or complex entries. Show that if A is normal and upper…

A: Definition of normal matrix:

Q: The 2 ´ 2 identity matrix is:

A: To find:

Q: 9. When can a square matrix be diagonalized? When can a square matrix be diagonalized orthogonally?

A:

Q: Let D = P'AP be a diagonal matrix, wher %3D Pesell thet if D:

A: Given, D=P-1AP be a diagonal matrix, where P is an orthogonal matrix. To prove that A is symmetric.

Q: 5. Is the matrix ㅇ 15 아가 Unitary? Explain. 블 ܐ ܥܙܐܡ ܝܐܐ ܙܐ3 춤을

A: A matrix is the arrangement of elements in a row and columns into a rectangular array. The order of…

Q: If Q and U are unitary matrices, show that Q-1 is unitary and also QU is unitary. Start from QHQ = f…

A: As per the question we are given two unitary matrices Q, U and we have to show that Q-1 , QU are…

Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

Q: 1. Consider the matrix and and Monde Cole 2022 202) Mesh Colleg 202C) Mona that 1 1 0 101 0 1 1 Mo…

A:

Q: Write y as the sum of a vector

A: Given,   And

Q: Determine the dimensions of Nul A and Col A for the matrices. A =

A:

Q: Let A and B be unitarily equivalent complex matrices. Show that A is normal if and only if B is…

A:

Q: 27. For any matrices A and B for which the product AB is defined, the (i,j)-entry of AB equals a¡bj…

A:

Q: 1) Suppose that A² = A and B is a diagonal matrix similar to A. Prove that B2 = B and that the…

A:

Q: -5 Let M = 5 . Find cj and c2 such that 3 M² + c, M + c2I, = 0, where I2 is the identity 2 ×2…

A: