Linear transformations-unique solutions

Assignment Help Mathematics

Reference no: EM13125152

Show that the system of equations

2x + y + z = -6a
2x + y + (b +1)z = 4
bx + 3y + 2z = 2a

Has a unique solution except when b = 0 and b = 6.

If b = 0, show that there is only one value for a for which a solution exists, and find the general solution in this case.

Discuss the case when b = 6.

Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.

Reference no: EM13125152

Questions Cloud

Illustrate what depreciation methods are available : A $4,000 computer to be used 100% for business located in his home. Illustrate what depreciation methods are available for the automobile and computer?

Rates-investments-systems of equations problem : A family made an investment for 1 year that earned $7.50 simple interest. If the principal had been $25 more and the interest rate 1% less, the interest would have been the same. Find the principal and the rate.

Explain why number can be described wit normal model : The number of smokers among 120 randomly selected students will vary from group to group. Explain why that number can be described wit a normal model.

What is the amount of nitrogen produced : Ammonia burns in pure oxygen and reaction produces nitrogen and water. What is the amount of Nitrogen produced from 45.0 g NH3?

Linear transformations-unique solutions : Discuss the case when b = 6. Interpret your solutions in terms of the kernel and image of the linear transformation T: o^3 --> o^3 represented by the equations.

The concentration of each gas once equilibrium is reached : The concentration of each gas once equilibrium is reached. The new equilibrium concentrations if the volume is suddenly halved (still at 298K)

Will sum of squared deviation scores be greater for test : Will the sum of squared deviation scores be greater for the test or the exam (assume the same number of people sat both the test and the exam)? Why?

American dream : Bret Harte, Mark Twain, Red Cloud and Sarah Hopkins are realistic writers. How do each of these writers see the "West" differently and similarly. How do they see its potential in terms of the "American Dream"?

Explain how were these obligations violated in hp case : The original lawsuit filed in the HP case claimed that the executives breached their fiduciary responsibilities. What are the fiduciary responsibilities of executives and members of the board of directors to shareholder? Explain how were these obl..

User Account

All Pages