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Suppose b,c 2 R, and T: R3 ! R2 deÖned as T (x; y; z) = (2x4 - y + 3z + b; 6x + cxy): Show that T is linear if and only if b = c = 0.
Check the local inevitability of the function f defined by f(x,y)=(x2-y2, 2xy) at (-1,1).Also step wise find a domain for the function f in which f is invertible and prove it.
Choose one type of matrix method (can be found in sections 6.2–6.6), describe the method, and give an example to illustrate how it might be used in a personal or professional scenario. In responding to your peers, comment on and ask questions about your classmates’ explanations of which method they would use for their particular application.
can you please help me I need to give an example on the matrix method and explain
Show that R 3 is a real vector space. Show that the set {(x, y, 0)|x, y ∈ R} is subspace of R 3 .
Check the local inevitability of the function f defined by f(x,y)=(x2-y2, 2xy) at (-1,1).Also step wise find a domain for the function f in which f is invertible and prove it.
Solve by gaussian method
X+2Y-3Y=11
3X+2Y+Z=1
2X+Y-5Z=11
Let U be the subspace of R5 denoted by U = (x1; x2; x3; x4; x5) in R5 : x1 = 3x2 and x3 = 7x4 : (a) Find a basis of U. (b) Find a subspace W of R5 such that R5 = U "\\bigoplus" W.
show that any g€l(v, c) and u€v with g(u) not equal to 0 v=null g i{£u:£€c
let V={(a,b,c)€R³|a+b=c} and W={(a,b,c)€R³|a=b} be subspaces of R³.Is R³ direct sum of V and W?
If A = ( 1,2,3) (5,6,7) (0,1,4) and B = (1,0,3) ( 5,6,1) (2,1,4) then find i) AB ii) Inverse of A & B
