Let A be an m x n matrix Suppose that is a (m k) x n matrix whose first m rows are the same as A Prove that kerC ker A Thus, appending more rows cannot increase the size of a matrix 's kernel Give an example where kerC ker A (2)

Question: Let A be an m x n matrix. Suppose that is a (m + k) x n matrix whose first m rows are the same

Let A be an m x n matrix. Suppose that

is a (m + k) x n matrix whose first m rows are the same as A. Prove that kerC Š† ker A. Thus, appending more rows cannot increase the size of a matrix's kernel. Give an example where kerC ‰ ker A

-(2)

Step by Step Solution

★★★★★

3.65 Rating (159 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Let r 1 r mk be the rows of C so r 1 r m are ... 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)

952-M-L-A-E (1873).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Let A be an m x n matrix. Show that (a) If x N(ATA), then Ax is in both R(A) and N(AT). (b) N(ATA) = N(A). (c) A and ATA have the same rank. (d) If A has linearly independent columns, then ATA is...

Let A be an m x n matrix, B an n x r matrix, and C = AB. Show that (a) N(B) is a subspace of N(C). (b) N(C)- is a subspace of N(B) and, consequently, R(CT) is a subspace of R(BT).

Let A be an m x n matrix of rank r and let |x1,..., xr} be a basis for R(AT). Show that {Ax1,. . . .. . ., Axr] is a basis for R(A).

Let A be an m x n matrix of rank r. (a) Suppose C = (A B) is an m Ã k matrix, k > n, whose first n columns are the same as the columns of A. Prove that rank C ¥ rank A. Give an example...

please help with these 6 practice problems 1 1 .LetA=[2 a space C(A), the null space N (A), the row space, and the left null space of A. . Find a such that rank A =1; and for this value of oz, nd...

please help me with questions problem 4 and problem 5 , which means all the questions included in the picture , I don't know why it keeps telling me I need to revise my question. there is no problems...

Problem 6.1. Let A be an m x n matrix, and suppose the CR factorization of A is A = CR, where C is an m x d matrix composed of linearly independent columns of A, and R is a d x n matrix in RREF...

Part A Let A and B be 4 x 4 matrices such that B'AB = 21. Suppose that det(B) = 3. Calculate det(A).(a) Suppose that W is a subspace of R" and that {u, v, w} is a basis for W. Prove that {u + w, v +...

The following is a general result from matrix theory: Let $\mathbf{A}$ be an $m \times n$ matrix. Suppose that the equation $\mathbf{A x}=\mathbf{p}$ can achieve no $\mathbf{p} \geq \mathbf{0}$...

these are questions for Linear Algebra, thanks for helping For each of the following statements either prove that the statement is correct, or provide a counterexample or a suitable proof that shows...

How should a house be designed to receive solar heat for (a) Winter-dominated (b) Summer-dominated climates? Why?

In 1917, Mahatma Gandhi settled a dispute between Indian farmers and British landowners. Under a share-cropping arrangement, each indigo farmer gave 15 percent of the harvest to the landowner. When...

All else being held equal, if a project's required rate of return increases, its NPV should increase. true or false

Lenders are always hurt by an increase in the inflation rate. Comment on the validity of this statement.

Let V denote the set of positive real numbers. Define the operation of scalar multiplication, denoted , by x = x for each x R+ and for any real number a. Define the operation of addition, denoted...

Let Z denote the set of all integers with addition defined in the usual way and define the scalar multiplication, denoted , by a k = [[]] k for all k Z where [[]] denotes the greatest integer less...

Let S denote the set of all infinite sequences of real numbers with scalar multiplication and addition defined by {an} = {an} {an} + {bn} = {an + bn} Show that 5 is a vector space.

Consider a firm that will produce one unit of gold a year from today. The price of gold next year is either 5 0 0 with probability p = 0 . 8 , or 2 0 0 with probability 1 - p . Assume gold price risk...

Bond X is a premium bond making semiannual payments. The bond has a coupon rate of 8.3 percent, a YTM of 6.3 percent, and has 16 years to maturity. Bond Y is a discount bond making semiannual...

Given 8 random bits forming a byte, can you determine whether the byte represents an integer or a character? Why?