Purchase Solution

Transformation matrix in vector calculus

Not what you're looking for?

Ask Custom Question

Section 6.1 The Geometry of Maps from R^2 to R^2.
Please see the attached pdf. file.

Let D* be the parallelogram with vertices...Find a T such that D is the image set of D* under T.

Attachments
Purchase this Solution
Solution Summary

The solution provides an example of finding a transformation matrix for a given situation.

Solution Preview

The solution is attached.

We need to find a map that takes the points to the points respectively.

However, it turns out to be much smarter to work in the opposite direction first - namely to find the linear ...

Purchase this Solution
Free BrainMass Quizzes
Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Probability Quiz

Some questions on probability

Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

View More Free Quizzes
Related BrainMass Solutions

  • Finding Derivatives : Fundamental Theory of Calculus and Chain Rule

    The coefficient matrix may have columns that are in the same plane. This also offers two possibilities. i) The vector b may be in the plane that the coefficient matrix columns are.

  • matrix of the composition

    Compare M3 to the standard rotation matrix about the origin (rotating a vector by angle  counterclockwise about the origin): Set and we get: The expert finds the matrix of the composition in the problem.

  • Linear transformation

    Say t is a linear transformation of a vector space V.

  • Transformation : Null Space, Range and Eigenvalues

    Since the null space of A3 is not (only) the null vector, that means the transformation is not one-to-one and, as a result, it cannot be a geometric transformation. Also, the image is not full R3, that means is not an on-to transformation as well.

  • Eigenvalues of a Transformation

    Write the transformation using matrices: x*T=v (vector x=(x_1, x_2, x_3); vector v=(x_1 - 3x_3, x_1 + 2x_2 + x_3, x_3 - 3x1_) and T is a [3*3] matrix with unknown elements.

  • Polynomials : Matrices, Reflection Matrices and Linear Transformation

    From the cubics P3 to the fourth degree polynomials P4, what matrix represents multiplication by 2 + 3t? The columns of the 5 by 4 matrix A come from applying the transformation to each basis vector x1 = 1, x2 = t, x3 = t2, x4 = t3.

  • Algebra: linear transformations and vectors

    , is a vector space. 2 Are the vectors x3 - 1, x2 - x and x linearly independent in P3 ?

  • Nilpotent transformation

    Describe the matrix which represents N with respect to the basis S. Please see the attachment. Consider the transformation N: V->V. Let g be a vector such that .

  • theory regarding diagonalization

    Solution: In the given problem, the matrix corresponding to the linear transformation is: [1 0 -3] [1 2 1] [-3 0 1] As you have already determined, the eigenvalues of this matrix are 2, 4, and -2.

View More Related Solutions