Question: Given a vector A, and two second order tensors Bij and Cij, prove that: (a) Fij = Bij + C is a second order

Given a vector A, and two second order tensors Bij and Cij,

Given a vector A, and two second order tensors Bij and Cij, prove that: (a) Fij = Bij + C is a second order tensor. (b) Hijk = AiBjk is a third order tensor. (c) B is a scalar. (d) Hijs = A, Bj; is a vector.

Step by Step Solution

★★★★★

3.48 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Solutions Step 1 In the expression FiBiCy where Fi is a vector Bi is a secondorder tensor and Cy is another secondorder tensor the result is a secondorder tensor By expressing it in index notation FiB... 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

Students Have Also Explored These Related Mechanical Engineering Questions!

Read the case study below and answer ALL the questions that follow. Lend Lease Case Study Lend Lease Corporation Limited is an Australian-based multinational company that specialises in project...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

OPEN QUESTIONS Question 1 Mutual funds Consider the regression output table 1.1 below which is the output of a Carhart 4-factor asset pricing model: Table 1.1 Y = + m*r+ smb*rSMB+ hml*THML+ mom *rOM....

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

The stock market data is given in the following table. Correlation Coefficients Telmex Telmex Mexico World 1.00 Mexico World SD (%) R (%) 1.50 1.00 18 ? 1.00 1.20 15 14 1.00 10 12 The above table...

Question 1 1 a Let { e 1 , e 2 } be a basis of a vector space V and let 2 vectors of V be U = 2 1 + 4 e 2 ; W = 5 e 1 + 3 e 2 Further, let e i o x e j be the basis vectors of E 4 = VoxV. ( i ) Find...

For the MATLAB script you write for this homework you should follow the documentation rules found in the Homework folder on BbLearn (in the Course Content tab). Use the MATLAB function publish to run...

doublePendulum v0.6 written by Alexander Erlich (mailto:alexander.erlich@gmail.com) Last update submitted to MATLAB File Exchange on October 5th, 2010. Lagrangian and di\u001berential equations The...

Tensor and Vector Calculus If you really know calculus I think you will know why the symbols mean:) 3:44 . . . Topic 1 - Preliminary Mathema... . . . Fourth rank or order (e.g. elastic tensor ) 4th...

Angie Silva has recently opened The Sandal Shop in Brisbane, Australia, a store that specializes in fashionable sandals. In time, she hopes to open a chain of sandal shops. As a first step, she has...

The Allowance for Impairment on Receivables in the accounts of Excel Co. at 1 October 2020 was $21,000 and the Receivables balance was $250,100. During the year, the business made total sales of...

The height ( in meters ) of a projectile shot vertically upward from a point 2 m above ground level with an initial velocity of 2 5 . 5 m s is h = 2 2 5 . 5 t - 4 . 9 t 2 after t seconds. When does...

A potential difference of 480 V is established between large, parallel, metal plates. Let the potential of one plate be 480 V and the other be 0 V. The plates are separated by d = 1.70 cm. (a) Sketch...

Figure shows two sections of an old pipe system that runs through a hill, with distances dA = dB = 30 m and D = 110 m. On each side of the hill, the pipe radius is 2.00 cm. However, the radius of the...

An air conditioner operates on 800 W of power and has a performance coefficient of 2.80 with a room temperature of 21.0oC and an outside temperature of 35.0oC. (a) Calculate the rate of heat removal...

A uniform solid sphere of radius R produces a gravitational acceleration of ar on its surface. At what distance from the sphere's center are there points (a) Inside and (b) Outside the sphere where...

Positive charge Q is uniformly distributed around a semicircle of radius a (Fig. 21.49). Find the electric field (magnitude and direction) at the center of curvature P.

What supply chain element involves the management of day-to-day tasks and risk management? Propose Plan Order Operations

Show that, as stated in the text, a force F exerted on a flexible medium at its center and perpendicular to its length (such as on the tightrope wire in Figure 4.16) gives rise to a FL tension of...

A carbon dioxide laser used in surgery emits infrared radiation with a wavelength of 10.6 m. In 1.00 ms, this laser raised the temperature of 1.00 cm 3 of flesh to 100C and evaporated it. (a) How...

Why do incandescent lightbulbs grow dim late in their lives, particularly just before their filaments break?

A testing laboratory studies and compares the relationship between tire tread wear per 1,000 miles (Y) and average driving speed (X) for two competing tire types (denoted A and B). The data shown in...

This problem involves the PERK study data discussed in Problem 12 in Chapter 8. Suppose that we want to compare the relationship between changes in refraction five years after surgery and baseline...

In Gruber's (1970) study of n = 104 individuals (discussed in Problem 10), the relationship between blood pressure change (SBPSL) and relative weight (RW), controlling for initial blood pressure...