QUESTION 5 P3(R), p(t)=1-2t?-t³, q(t)=t +2t3, r(t)=1+t- 2t? are linearly independent. The 3 vectors of True False

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

A:

Q: 8. If {V1, V2,..., ,}is a linearly dependent set of vectors, prove that one of these vectors is a…

A:

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

A:

Q: and ā is a cC 7) will be

A:

Q: 6. Determine if the vectors vị = (1, -1,3, –1), v2 = (1, –1, 4, 2), v3 = (1, -1,5, 7) dependent or…

A: We have to find that given vectors are linearly dependent  or linearly independent.

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: (a) Show that the vectors v = and w = 2 are linearly independent. (b) Explain why 3 vectors in R" of…

A:

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: 18 as a linear combination of a and y Express the vector v y.

A:

Q: Find the length of the vector x=x= |x|=|x|=

A:

Q: 3 -1 V3= 4 3 4 -2 2. 2.

A:

Q: 5.) Let V₁ = - -2 V₂: Is b a linear combination X₁V₁ + x₂ V₂ = b. 5 b=4 of v₁ and v2; that is, does…

A: Here we have to check whether the given vector b→=745 is linear combination of vectors v1→=1-2-5 and…

Q: Let v1 = (-6, -6, -9), i2 = (3, 3, 12), iz =(-1,-1,6). Are the vectors v1, 02 and vz linearly…

A: See the attachment

Q: Two linearly independent vectors in R3 span R2, is that true

A:

Q: Every vector of R²is linear combination of (-1, 1), (2, –2)? Justify

A:

Q: Find the stable vector of 7 P = 2/7 M5 iii

A:

Q: The vector v = -2 is orthogonal with 1 a) (-1 -6 7) b) (-1 6 -7) c) (-1 -6 -7) d) (1 -6 -7)

A:

Q: Are the vectors 16 + 16x – 12x2, linearly independent + - 12 – 12x – 12x2 and 18 + 18x – 3x2…

A:

Q: Find two linearly independent vectors perpendicular to the vector 2 -5 -9 D =

A: Two vectors are said to be perpendicular to each other if and only if their dot product is zero.

Q: Find the stable vector of 0 0 1 1 P 2 1 3 3 ..-

A: It is an important part of statistics. It is widely used.

Q: 9. Explain why four vectors is R³ are always linearly dependent.

A:

Q: 3 Consider the vectors a= =(2³₁) and b =(p+¹). 2p 8 Find the possible values of p for which a and b…

A: we have to find p.

Q: Are the vectors V₁ = 2 1 1 V₂ = 1₂V3 3 4 1 linearly independent? -9

A:

Q: 2 A : 10 %3| 0 -1 4

A: To find out solution of homogeneous set of linear equation of A's we have to find the solution of…

Q: Find the value of k for which the vectors 4 4 -5 X = || = 4 and y = 0 1 -2 k are orthogonal.

A:

Q: It is known that two vectors are equal and represented by A- (2+3x)i + 11j and B- -7i + (3x + 2y)j…

A: if two vectors are equal then coefficients of I and j are same.

Q: 7. Find all values of x that make (x, 1, –3) and (x, 2, x) perpendicular vectors.

A: I am attaching image so that you understand each and every step.

Q: 21 -2 and y -3 3 Express the vector v as a linear combination of a -4 y.

A:

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

A:

Q: If a = (4, 0, -1), find a vector b such that comp₂b = 3. b = X

A: a=<4,0,-1>ab=3ab=a→.b→a→let b=<b1,b2,b3>

Q:

A:

Q: 5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b)…

A: The objective of this question is to determine whether the given sets of vectors are dependent or…

Q: Show that the vectors X1 = 2e2t and 2et X2 5e3t form a linearly independent set.

A: