Show that u = (a, b) and v = (e, d) in K? are linearly dependent if and only if ad – be = 0.

Q: ii) Show that any four vectors oj, , 5, Vi in R are linearly independent.

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = √(x2 + y2 +…

A: Given: Function f(x,y,z) as follows: and a point (1,2,2) To find: Linearization L(x,y,z) of the…

Q: Is {x² – 2.x, x²+x, x²} linearly independent dependent? Prove your answer. or

A: Answer

Q: Show that the functions f, (x) = 4x" , and f2(x) = x"** are linearly independent on (-00, 00).

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {−2 −…

A: Given set is Consider

Q: Show that the set {1, x, x2, ... , xn} is linearly independent in Pn(F).

A: Given, {1, x, x2, ... , xn}

Q: b = Find whether {a, b} linearly independent or not. 5. Let a are

A: Given a = 20 , b = 07

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent.S = {1 + 3x…

A:

Q: Let u = (2,3, 1), v = (1,3,0), and w = (2,23, 3). Since (1\2)u – (2\3)v – (1\6)w = (0,0,0), can we…

A: No we can't

Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

A:

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, 32, ..., Yn)(to) #0…

A: If two functions are linearly dependent then the Wronskian is zero for every value of t.

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {1 +…

A:

Q: Find the values of for which :=,0) and": =(a.1) are 4a-4 linearly independent in *".

A: To find the values of a for which the below vectors are linearly independent in R2. v1=4a−4, av2=a,…

Q: Find the linearization of f(r, y, z) = x + y² + z³ at the point (1, 2, -1).

A:

Q: Suppose u1, ūz and ūz are linearly independent. Let īj = ủ1+ ủ2, 02 = ủ1 + ủ3 and ī3 = ū2 + 2ūz.…

A: Given: Let u1→,u2→,u3→ are linearly independant. Let v1,→=u1→+u2→,v2,→=u1→+u3→,v3→=u2→+2u3→

Q: Are the functions f(x) = e ^x and g(x) = e ^|x| linearly independent on I = (−1, 1)? Are they…

A:

Q: If {v1, v2, . . . , vn} is a linearly dependent set of vectors, prove thatone of these vectors is a…

A:

Q: Give an example of three linearly dependent vectors in R3 such that none of the three is a multiple…

A:

Q: Find the linearizations L(x, y, z) of the functions at the given points. ƒ(x, y, z) = x2 + y2 + z2…

A: given that a function f(x,y,z)=x2+y2+z2 we need to find the linearizations of f(x,y,z) at (1,1,1).…

Q: The functions y1, 2, ..., Yn are linearly independent, if and only if W (91, 32, ..., Yn)(to) #0 for…

A:

Q: Prove that if {Vi, V2, v3} is linearly independent, then so too is the set {u, u2, u3 where u = V -…

A: Introduction: Linear dependence and linear independence of a given number of vectors are very…

Q: Give examples of two sets of vectors in P3 such that one of them is linearly independent and another…

A:

Q: If S and T are normal linear operators satisfying ST* = T* S and TS* = S*T, show that their sum S+T…

A: I have used just definition of normal operator

Q: Show that the functions e^x , e^2x , e^3x are linearly independent.

A:

Q: The functions y1, Y2, . .. , Yn are linearly independent, if and only if W (y1, Y2, ..., Yn)(to) # 0…

A: We can use the Wronskian test to check the functions are linearly independent or dependent.

Q: The set of all linearly independent solutions of D.E yY-y 0 is Select one: a. (1,t,e',e ) b.…

A:

Q: Two vectors in R2 are linearly dependent if and only if they lie on a line through (0,0). Select…

A: We have to check it is true or false  Two vectors in R2 are linearly dependent if and only if they…

Q: Consider x1 = et and x2 = v(t)et. If x1 and x2 is linearly independent, then v′(t) = 0. Is this…

A:

Q: 5. Conclude from this that if b x c = 0 then b is a scalar multiple of c or vice versa (b and e are…

A:

Q: {(0,0,0), (3,5,6) ) is linearly dependent in R ulgn O İhi O

A: Given {(0,0,0),(3,5,6)}

Q: Prove that if {u, v} is linearly independent, then so too is {u+ v, u - v}.

A:

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: Show that the functions y1= e^t,  y2 = e^-t, and te^-t are linearly independent.

A:

Q: (d) Let A E M3x3(R) and , ij, Z ɛ R* and they are linearly independent. Suppose that we have A = ,…

A:

Q: Suppose v1, ..., Vm is linearly independent in V and w e V. Prove that if vi + w, ..., Vm +w is…

A:

Q: Determine whether the set of vectors in P2 is linearly independent or linearly dependent. S = {1 +…

A:

Q: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

A: The vectors u=[-3, -4, -17]T , v=[3, 0, -6+k]T, w=[-1, 2, 1]Tare linearly dependent if and only if k…

Q: Prove that if (V1,V2, V3} is linearly independent, then so too is the set (u,u2, u3} where u, vı-…

A:

Q: Suppose vi, v2, ..., m is linearly independent in V and w ɛ V. Show that v1, vz, ..., Um, W is…

A: v1, v2,......., vm is linearly independent in V and w∈V

Q: Check the set 4 2 3 Mas(R) = 11 is linearly dependent or linearly independent

A:

Q: Find the value of x so that the following are linearly dependent in R³. (1, –1,0), (-1, x, 0), (0,2,…

A:

Q: Show that the set {1, x, x2, ..., xn} is linearly independent in Pn(F).

A:

Q: 3. Determine whether the functions e and re are linearly independent or dependent by calculating…

A: f= {e^2x , x.e^2x} is Linearly independent if Wronskian is non zero.

Q: Show that the functions f (x) = |x + 1|and g(x) = x² are linearly %3D independent on the interval I…

A: Given that f(x)=|x+1| So, f(x)=x+1 in [1, ∞) g(x)=x2

Q: Suppose that T: R2→ R2 is linear, T(1, 0) = (1, 4), and T(1, 1) = (2, 5). What is T(2,3)? Is T…

A: Given,

Q: Let u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). Since (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

A: Given: u = (2, 3, 1), v = (1, 3, 0), and w = (2, -3, 3). And, (1/2)u - (2/3)v - (1/6)w = (0, 0, 0),…

Q: Show that {x, y} is linearly dependent if and only if x or y is a multiple of the other.

A: It is given that, x and y are two distinct non-zero vectors.

Q: If v1, ..., V5 are in R' and v3 = 0, then {v, V2, V3, V4, V5} is linearly dependent. %3D

A: Definition used: v1, v2, ..., vk is linearly dependent if there exist numbers α1, α2, ..., αk, not…

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.