The bases and dimensions for the four subspaces associated with A and B. A = [ 1 2 4 2 4 8 ] and B = [ 1 2 4 2 5 8 ] . For A, The row space basis is row 1 = ( 1 , 2 , 4 ) , nullspace is ( − 2 , 1 , 0 ) and ( − 4 , 0 , 1 ) The column space basis is column 1 = ( 1 , 2 ) , left nullspace is ( − 2 , 1 ) For B, The row space basis both rows are ( 1 , 2 , 4 ) and ( 2 , 5 , 8 ) , nullspace is ( − 4 , 0 , 1 ) The column space basis two columns are ( 1 , 2 ) and ( 2 , 5 ) , left nullspace basis is empty . Given: A = [ 1 2 4 2 4 8 ] and B = [ 1 2 4 2 5 8 ] Calculation: Consider matrices A = [ 1 2 4 2 4 8 ] and B = [ 1 2 4 2 5 8 ] For A, the row space basis is row 1 = ( 1 , 2 , 4 ) , nullspace is ( − 2 , 1 , 0 ) and ( − 4 , 0 , 1 ) , column space basis is column 1 = ( 1 , 2 ) , left nullspace is ( − 2 , 1 ) For B, the row space basis both rows is ( 1 , 2 , 4 ) and ( 2 , 5 , 8 ) , nullspace is ( − 4 , 0 , 1 ) , the column space basis two columns is ( 1 , 2 ) and ( 2 , 5 ) , left nullspace basis is empty as the space contains only y = 0 that means the rows of B are independent.

Question

learn.edgenuity : C&C VIP Unit Test Unit Test Review Active 1 2 3 4 Which statement is true about the graph of the equation y = csc¯¹(x)? There is a horizontal asymptote at y = 0. उद There is a horizontal asymptote at y = 2. There is a vertical asymptote at x = 0. O There is a vertical asymptote at x=- R Mark this and return C Save and Exit emi

Answer 1

Question

Chapter 3.5, Problem 2PS

To determine

The bases and dimensions for the four subspaces associated with A and B.

A=[1 2 42 4 8]and B=[1 2 42 5 8].

For A,

The row space basis is row 1=(1, 2, 4), nullspace is (−2, 1, 0)and (−4, 0, 1)

The column space basis is column 1=(1, 2), left nullspace is (−2, 1)

For B,

The row space basis both rows are (1, 2, 4) and (2, 5, 8), nullspace is (−4, 0, 1)

The column space basis two columns are (1, 2) and (2, 5), left nullspace basis is empty.

Given:

A=[1 2 42 4 8]and B=[1 2 42 5 8]

Calculation:

Consider matrices A=[1 2 42 4 8]and B=[1 2 42 5 8]

For A, the row space basis is row 1=(1, 2, 4), nullspace is (−2, 1, 0)and (−4, 0, 1), column space basis is column 1=(1, 2), left nullspace is (−2, 1)

For B, the row space basis both rows is (1, 2, 4) and (2, 5, 8), nullspace is (−4, 0, 1), the column space basis two columns is (1, 2) and (2, 5), left nullspace basis is empty as the space contains only y=0that means the rows of B are independent.

Expert Solution & Answer

Trending nowThis is a popular solution!

See solution

Check out sample textbook solution

Students have asked these similar questions

learn.edgenuity : C&C VIP Unit Test Unit Test Review Active 1 2 3 4 Which statement is true about the graph of the equation y = csc¯¹(x)? There is a horizontal asymptote at y = 0. उद There is a horizontal asymptote at y = 2. There is a vertical asymptote at x = 0. O There is a vertical asymptote at x=- R Mark this and return C Save and Exit emi

ے ملزمة احمد Q (a) Let f be a linear map from a space X into a space Y and (X1,X2,...,xn) basis for X, show that fis one-to- one iff (f(x1),f(x2),...,f(x) } linearly independent. (b) Let X= {ao+ax₁+a2x2+...+anxn, a;ER} be a vector space over R, write with prove a hyperspace and a hyperplane of X. مبر خد احمد Q₂ (a) Let M be a subspace of a vector space X, and A= {fex/ f(x)=0, x E M ), show that whether A is convex set or not, affine set or not. Write with prove an application of Hahn-Banach theorem. Show that every singleton set in a normed space X is closed and any finite set in X is closed (14M)

Let M be a proper subspace of a finite dimension vector space X over a field F show that whether: (1) If S is a base for M then S base for X or not, (2) If T base for X then base for M or not. (b) Let X-P₂(x) be a vector space over polynomials a field of real numbers R, write with L prove convex subset of X and hyperspace of X. Q₂/ (a) Let X-R³ be a vector space over a over a field of real numbers R and A=((a,b,o), a,bE R), A is a subspace of X, let g be a function from A into R such that gla,b,o)-a, gEA, find fe X such that g(t)=f(t), tEA. (b) Let M be a non-empty subset of a space X, show that M is a hyperplane of X iff there Xiff there exists fE X/10) and tE F such that M=(xE X/ f(x)=t). (c) Show that the relation equivalent is an equivalence relation on set of norms on a space X.