Question: In R3 the shear in the xy-direction with factor k is the linear transformation that moves each point (x, y, z) parallel to the x-plane

In R3 the shear in the xy-direction with factor k is the linear transformation that moves each point (x, y, z) parallel to the x-plane to the new position (x + ky, y + kz, z)- (See the accompanying figure.)
Find the standard matrix for the shear in the xy-direction with factor k.

Ox+kz, y + kf)

Step by Step Solution

★★★★★

3.50 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

The matrix whi... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

938-M-L-A-E (1451).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Find the standard matrix for the linear operator T: R3 R3 that maps a point (x, y, z) into Its reflection through the xz-plane

Find the standard matrix for the linear operator T: R2 R2 that maps a point (x, 7) into (see the accompanying figure) (a) Its reflection about the line y = -x (b) Its reflection through the origin...

Suppose that a point (X, Y, Z) is to be chosen at random in three-dimensional space, where X, Y, and Z are independent random variables and each has the standard normal distribution. What is the...

4 This assignment, based on the content of Unit 4 of the Study Guide, is worth 3% of your grade. We recommend that you hand it in after you complete Unit 4. You must show all of your work in order to...

summarise that article and make it to 2000 words Your report should clearly contain 4 main Parts: Introduction, Literature Review, Result and Analysis, Conclusion. The Challenge of Setting Standards...

seventh pages Chapter 3 Curve Sketching How much metal would be required to make a 400-mL soup can? What is the least amount of cardboard needed to build a box that holds 3000 cm3 of cereal? The...

A creative engineer suggests structuring the TLB so that not all the bits of the presented address need match to result in a hit. Suggest how this might be achieved, and what might be the costs and...

For example, when a ball is thrown into the air, it gains kinetic energy as it moves upward. As it reaches the top of its trajectory, this kinetic energy is converted into potential energy. When the...

the air, it gains kinetic energy as it moves upward. As it reaches the top of its trajectory, this kinetic energy is converted into potential energy. When the ball falls back to the ground, the...

as it moves upward. As it reaches the top of its trajectory, this kinetic energy is converted into potential energy. When the ball falls back to the ground, the potential energy is converted back...

Record the following transactions in the appropriate ledgers of TRY ME LIMITED and extract a Trial Balance as at 31/12/2020 December 1 Deposited an amount of GHS500,000 into a business bank account...

Zabala Auto supply has the following transactions during the month of January, 2030: You are hired to prepare the financial statements for the month of January 2030: 1 Mr. Zabala invested P1,500,000...

In blow program, which lines have bugline 1 4 and line 6 line 1 3 and line 1 1 line 1 3 and line 6 line 1 4 and line 1 3

3. Read the following sentence and explain whether the economic logic is correct or incorrect: If Icelands government reduces its discretionary spending to balance the budget, then the nations...

Let A be a nonnegative irreducible 3 3 matrix whose eigenvalues satisfy 1 = 2 = |2| = |3| = Determine 2 and 3.

Let where B and C are square matrices. (a) If Î» is an eigenvalue of B with eigenvector x = (x1,..., xk)T, show that Î» is also an eigenvalue of A with eigenvector = (x1,...,...

If A is an n n matrix whose eigenvalues are all nonzero, then A is nonsingular. In the case of a true statement, explain or prove your answer. In the case of a false statement, give an example to...

Empathy among police officers influences how they interact with citizens and the likelihood that they receive complaints. Gender differences in levels of empathy in the general population are not...

There are a number of taxation rate structures in use in various countries in the world. For citizens residing in the United States, a progressive tax rate structure is applicable presently. In...

Down Under Boomerang, Inc., is considering a new three-year expansion project that requires an initial fixed asset investment of $2.97 million. The fixed asset falls into the three-year MACRS class....