7 Answered Questions for the topic Linear Transformation

Linear Transformation Linear Algebra Matrices Diagonalizable


Please, help-me with this Linear Algebra question

If T:R4→R4 is an linear transformation and pT(t) a characteristic polynomial of T, which of these options T is diagonalizablea) pT(t) = t^4 - 1 b) pT(t) = t^3(t + 2) c) pT(t) = t^2(t^2 - 1) d)... more
Linear Transformation Calculus


Calculus Linear Transformation

Fix x ̄ = (x1,...,xn) ∈ Rn. Define f : Rn → R such that f(y ̄) = ⟨y ̄,x ̄⟩. Show f is a linear transformation.
Linear Transformation Linear Algebra Matrix Standard Matrix


Linear Transformation and Standard Matrix

Let T: R2-> R2 be the linear transformation with the property: T(1, 0) = (4, -1) and T(2, 1) = (6, 1)Find [T], the standard matrix of T
Linear Transformation Linear Algebra Matrix True Or False


True or False: Linear Transformation & Matrix

Determine which are true and which are false:A) If there is a path of lenght 2 between two specific vertices in an undirected graph, then there must be a path of lenght 3 between those two... more
Linear Transformation Linear Algebra


Linear Transformation Questions

Suppose that T : R2 -> R2 is a linear transformation satisfying T(e1) = (5, 4) and T(e2) = (3, -2). Compute the following:(a) T(2, 0)(b) T(1, 1)(c) T(2, -3)
Linear Transformation Linear Algebra


Is there a linear transformation where the kernel has dimension 2. Is this transformation unique?

Is there a linear transformation where the kernel has dimension 2? Is it unique?
Linear Transformation


Determine the rotation matrix that rotates 3-vectors through an angle of 300 in the plane x1 + x2 + x3 = 0.


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