Let X ∈ R3 be some xed vector with coordinates X1, X2, X3. Consider the action on vectors of the operator “cross-product by X”. In other words, it transforms vectors using the rule v → X × v. Since this is a linear operator, it is represented by some 3 × 3 matrix. Find this matrix in terms of X1, X2, X3. Is this matrix ever invertible?

Q: A is a matrix and there's a vector x, and Ax is defined. Can the equation Ax=0 have no solution ?…

A:

Q: Consider the matrix attatched and the vector u = (2 0)*. Let B=(A−AT)2 and define vector v = Bu. If…

A:

Q: Let A, B, and C be invertible matrices of the size. Prove that (ABC)" == ("B"A" same size,

A:

Q: Let A, B, and A+B_ all be square invertible matrices of the same size. Show that (A +B')' = A(A+B)'…

A:

Q: Write the standard matrices of the given linear operators: a) L1(x) = (X1 +x2, X2 – X1) b) L2(x) =…

A: a. we have L1(x)=(x1+x2,x2-x1)  we take standard ordered basis β= (1,0),(0,1) and β=…

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

A:

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: 47. Prove that if A and B are square matrices and AB is invertible, then both A and B are…

A:

Q: Use matrix multiplication to find the contraction of (a, b) with factor k = 1/α, where α > 1.

A:

Q: entries

A:

Q: 1. Let ƒ : R³ → R5 be the function given by f(x₁, x2, X3) = (x₁ + x2 − X3, 2x1 + 2x2 − X3, 3X1 + 3x2…

A: