Suppose you know that every vector in R° can be uniquely written as a linear combination of vectors in a set S. What can you conclude about S? O A. S has exactly 5 vectors. O B. S has at most 5 vectors. O c. S has at least 5 vectors. O D. S could have any number of vectors.

Q: 2.Show that the following Vectors form a Wasis tor Pg. 4.ct-11.(t-1",(t-1'

A:

Q: Q2 (a) Let n E N and let 7, w e R". Show that if ở - = 0, then || † + w||? = || T||? + ||||?. (b)…

A: To answer the given question we shall use the following rule: 1.   If x→∈ℝn, then…

Q: Given the following set of the vectors from M22 0 3 (46 S= (2 1)( 8 6 )} 46 We can express as a…

A:

Q: 4. Suppose the vectors u and w are in space R, then u - 2w and u+ 2w are perpendicular if (a) ju =…

A: Our guidelines we are supposed to answer only one question. Kindly repost other question as the…

Q: For what values of b are the given vectors o , (smallest value)

A: Let m→=-12, b,3 and n→=b, b2,b  If m→ and n→ are orthogonal.

Q: Given that a = (1,1) and b = (-1,0). Find a vector in the same direction as but a+b five times as…

A:

Q: Consider the following vectors: -1 -3 -2 3 -3 4 8 For each of the following vectors, determine…

A:

Q: For which value of a , the vectors î +} – k , î – 2î + 3k and 3î + a ĵ+ 5k are coplanar? -3 O 3 O 4

A: The given three vectors are                                              A→=i^+j^-k^…

Q: Given the 3 vectors u, v and w in 3 dimensional space. If v→·(u→×w→)=0 which of the following…

A: Introduction: Suppose three vectors a→,b→,c→ are provided. Then, their scalar triple product is…

Q: for what h is the following collection of vectors linearly dependent? (see attached picture)

A:

Q: 3. Determine whether each vector can be written as a linear combination of the vectors in S = {(6,…

A:

Q: Q2 (a) Let n E N and let ở, w e R". Show that if ở · w = 0, then || ở + w||2 = || ||² + ||w||². (b)…

A: This question can be solved using the concept of dot product of two vectors.

Q: (d) Let u, v, w be arbitrary vectors in R³. What does the set of all combinations, Cu + c2v + C3w,…

A:

Q: Given the set of vectors S = -2.77 0 {[][][]} 4.9 0 3.1 of the following statements, if any, are…

A:

Q: Given K= (-2,-1), L=(2,4), M= (-3,-1) and N= (1,4), Prove that KĽ and MN are equivalent by Showing…

A: Two vectors are Equivalent if they have same magnitude and direction.

Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select…

A:

Q: Mark the following statement true or false:

A: Given statement is "in R3 if a set of vectors can be drawn head to tail one after the other so that…

Q: Given the following set of the vectors from M22 1 1 1 0 0 3 46 S = 2 1 0 2 21 8 6 46 We can not…

A:

Q: Given the following set of the vectors from M22 1 1 10 0 3 4 6 21 0 2 2 1 8 6 4 6 We can not express…

A:

Q: Find a and b such that v = au + bw, where u = ⟨1, 2⟩ and w = ⟨1, −1⟩. v = ⟨4, 5⟩

A: we have to find a and b such that v=au+bw where u=1,2 and w=1,-1 and v=4,5. the given vectors are:…

Q: If W is the set of all vectors of the a form 0, where a is a real [B] -1 number. Then, which of the…

A:

Q: Which of the following sets of vectors is a basis for R?? {}E} 2

A:

Q: For what value of k, the vectors (-1,0,1), (2,1,A) and (3k+2, 3,10) are lincarly dependent. O A. 1…

A: We have to find for what value of k, the vector -1,0,1, 2,1,4, and 3k+2,3,10 are linearly dependent.

Q: 2. Which of the following sets of vectors are linearly independent? 1 900)

A: Let us check linearly independent set as shown below

Q: Suppose S is a set of R vectors, and you know that every vector in span S can be written uniquely as…

A: Consider the given information.

Q: the following subset of Pz CTR). S=2x²+3x-1, x²+x-1,x²-3x -13. LET be Determine if S is lin, dep, +…

A:

Q: (à) If éách véčtór in V can be expressed uniquely as a linear combination of vectors in S, then S is…

A:

Q: Suppose Q : R? → R is a quadratic form such that Q(x) = 1 for all vectors X E R? Cuch that

A: Given: It is given that the quadratic function Q:R2→R such that Q(x)=1 for all vectors x∈R2 such…

Q: write the following vectors as linear combinations of e1, e2 and e3

A: What is Linear Combination: For a given vector v∈VF, it is referred to as linear combination of…

Q: Let 7 and w be vectors in R". Prove that If |7| = |7| = | 7 + |, then |7 - wf=3|7

A:

Q: Consider the set C² : 21, 2 Define the vectors of ū, ū, w E C² = () 2 2i = -1+3i -2+i (a) Evaluate…

A: ℂ2=z1z2/z1,z2∈ℂu→=21-i, v→=2i-1+3i, w→=-1+i-2+i

Q: Let u, v, w1, w2, and w3 be vectors in Rn. If u and v can both be written as linear combinations of…

A: According to the given information, Let u,v,w1,w2,w3 be vectors in Rn and u and v can be written as…

Q: Suppose A is equal to the following: A= 1 3 2 -1 2 -6 2 2 a) Determine N(A), the nullspace of A.…

A:

Q: For which je{1,2,3,4} do we have ||A||₁||Aejl|₁, when O a. none A = O b. j=1 O c. j=2 d. j=3 O e.…

A:

Q: Consider the following vectors á = 2ī+3j and b = -2ī+ 3k and c = −3ī + k

A: topic- projection of one vector on another

Q: Suppose you know that every vector in R can be written as a linear combination of the vectors in a…

A: The set has at least 5 vectors otherwise it will not span the set R5.

Q: Given vectors a, b E R" for integer n > 1, show that ||a + b||? + ||a – b| = 2||a||? + 2||b||? What…

A:

Q: A vector collinear to ū= is: a. d. 1,-2,-3> b. -1,2,3 > e. [K C.

A: Solution is here

Q: What conditions must a and b obey in order to make all vectors u = (ui uz uz)", such hat and bu to…

A:

Q: 1) Let ū = (1,3, -4), ở = (5, –6, 2), w = (-4, 3, 1) a) Compute the linear combination 2u – 70 + 4w…

A: Let u→=1,3,-4 and v→=5,-6, 2 and ω→=-4,3,1

Q: For what values of a is the vector (a2, a, 1) belongs to span {x1 = (1,2, 3), x2 = (1,1,1), x3 =…

A:

Q: If the vectors ai + j+ k, i + bj + k and i +j+ ck (a # b ± c ± 1) are coplanar, then the value of…

A:

Q: 3- Given a vector A (r 17.5, 0= 90°, o = 55") and vector B (r=17.5, 0= 40°, q = 55") the distance…

A:

Q: For which je{1,2,3,4} do we have ||A||=||Aejlloo, when O a. none A = O b. j=1 O c. j=2 d. j=3 O e.…

A:

Q: Is the following set of vectors in P, is linear independent? Prove the answer. {1+ 3x + 3x²; 1 – 2x…

A: The vectors are linear Independent.

Q: Given the following: P2(5, 2, –4) to P,(3, –1,0), Determine the vector R21.

A:

Q: • (d) Suppose a, b, c are non-zero vectors in R2, and a is perpendicular to both of b, c. Then b and…

A:

Q: Find a and b such that v = au + bw, where u = (1, 2) and w = (1, -1). = (5, 4) a =

A: It is vector problem.

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.