The vectors [1, 0, 1], [1, 1, 1] and [1, 0, -1] are coplanar. True False

Q: (1, Find a vector orthogonal to both (3, 2, 0) and to (0, 2, -1) of the form

A: The given question is related with vector space. We have to find a vector orthogonal to both 3 , 2 ,…

Q: The vectors u=(1,-2,1), v=(3,0,-2) and w-(5,-4,0) are: O not coplanar coplanar

A: We can check whether the three vectors are co planar  or not as below

Q: Consider the vectors [2, 1,0, 2|], [3, 1,0, 1), [1,1, 0, -1] in R. Decide whether they independent.…

A:

Q: The vectors (3,-4,1) and (5,3,3) are orthogonal. True False

A: Topic - vector

Q: Find the norm of the vector U(2,-6,1)

A: See the solution below.

Q: Determine a vector that is orthogonal to both (1, 2, -1) and (3, 1, 0).

A:

Q: Determine a vector that is orthogonal to both (1, 4, −1) and (5, 1, 0).

A:

Q: Consider the vectors (2, 1, 0, 2], [3, 1,0, 1], [1, 1, 0,-1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: How do I show that the vectors (1, 2), (0, 1), (-3, 4) are not linearly independent?

A: To verify that the three given vectors in the plane are linearly dependent

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: 3. Show that the vectors v, = (0, 3, 1, -1); v, = (6, 0, 5, 1); v; = (4, -7, 1, 3) form a linearly…

A:

Q: Find all vectors in R' that are perpendicular to both [1,0, 1, 0] and [1,2,0, 1] and then find a…

A:

Q: Show that the column vectors (1,1,2,4), (2,-1,-5,2), (1,-1,-4,0) and (2,1,1,6) vectors in R are…

A:

Q: 3. Give two nonparallel vectors that are both orthogonal to (0, 5, 0).

A: Given A = (0,5,0) Let other two vectors be of type B = (a,b,c) A.B = a.0+b.5+c.0 A.B = 5b For…

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: 6- which of the vectors X-(1,2),Y =(0,1),Z =(-2,-4 ) ,W=(-2,1), U=(-6,3) are orthogonal ,in same…

A:

Q: Determine whether the given vectors (1, 1,-1, 1), (1,-1, 2,-1), (3, 1, 0, 1) in R* are lincarly…

A: Given vectors are: (1, 1, -1, 1) , (1, -1, 2, -1) , (3, 1, 0, 1) We have to determine whether the…

Q: Are the vectors (-3,0,4), (5,-1,2), and (1,1,3) linearly independent in R3?

A:

Q: 3. Show that the vectors v = (0, 3, 1, -1); v, =(6, 0, 5, 1); v, = (4, -7, 1, 3) form a linearly…

A: Given the three vectors

Q: Find a vector that is orthogonal to (−1, 2, 2)

A: Find a vector that is orthogonal to (−1, 2, 2)

Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

A:

Q: 1. For non-zero vectors, a and b, show that axb =a5-(ā • 5} . %3D

A: For non-zero vectors a→ and b→ we have to show that: a→×b→2=a→2b→2-a→·b→2 Assuming, a→=ib→=j Putting…

Q: Show that the vectors (1, 1, 1), (1, 2, 3) and (3, 3, 4) are linearly independent?

A:

Q: Find a vector orthogonal to both and

A: Given query is to find the vector orthogonal to the given vectors.

Q: Find two unit vectors orthogonal to both (3,2,1) and (–1,1,0).

A: The vectors 3,2,1 and -1,1,0

Q: Find all orthogonal vectors to u=(2, -3).

A:

Q: Show that the column vectors (1,1,2,4),(2,-1,-5.2) (1,-1,-4,0) and (2,1,1,6) vectors in R are…

A:

Q: 2. Write the vector v = (1,3,2) as a linear combination of vectors u = (1,2,1), %3D (2,6,5), uz =…

A: We have to write a vector v to a linear combination of the vectors u1, u2, u3

Q: The vectors (3, –4,1) and (5,3,3) are orthogonal. True False

A:

Q: 20. Find two vectors of norm 1 that are orthogonal to the vectors u = (2,1,-4,0), v = (-1,–1,2,2),…

A: To find two vectors of norm 1 that are orthogonal to the below vectors.…

Q: 4. Give an example of vectors in R3 that spans R3. (show works)

A:

Q: Find the length of the vector.v = (2, 0, −5, 5)

A:

Q: Show that the vectors , and are coplanar.

A:

Q: b) Express the vector (–1,5, -6) in R³ as a linear combination of (2,0, 7), (2,4, 5) and(2, –12,13).

A: See the detailed solution below.

Q: What is the value of each of the constants that are part of the linear combination between the…

A:

Q: 4. Write the vector (1, 2, –2) as the sum of two vectors: one that is parallel to the vector (1, 1,…

A:

Q: Show that the vector a= (2, – 5, 3) in V, (R) can not be expressed combination of the vectors a, =…

A:

Q: Express the vector (2, –5, 3) in R³ as a lincar combination of the vectors (1.-3, 2), (2, –4, -1)…

A:

Q: What must be a if the vectors (1,-a,1,1). (-1,a+2,–2, a –1), (0,2, –1,a² +a-4) are linearly…

A: We have to solve given problem:

Q: Show that the column vectors (1,1,2,4), (2,-1.-5.2), (1.-1,-4,0) and (2,1.1,6) vectors in R are…

A:

Q: 2- We can write the vector x = (19,–1, -) in R³ as a linear combination of the vectors x1 =…

A:

Q: Make the vectors u1=(2,0,-1,1), u2=(1,1,-1,3), u3= (-1,1,1,-1) orthonormal.

A:

Q: Find a vector orthogonal to both (-4,-4,0) and to (0,-4,-4) of the form (100)

A:

Q: Let u, = (1,1,1)", u2 = (1,2,2)T and uz = (2,3,4)", find the coordinates of the vectors (2,3,2)" and…

A: Solving by linear combination method

Q: Find a vector of norm 1 that is orthogonal to the three vectors u = (2,1,-4,0), =(-1,-1,2,2),…

A: The solution is given as

Q: Consider the vectors (2, 1,0, 2], (3, 1,0, 1], [1, 1,0, -1] in R'. Decide whether they independent.…

A: Given: Vectors in ℝ4,                              2,1,0,2, 3,1,0,1, 1,1,0,-1 To find: Whether the…

Q: Show that the vectors (1,1,0), (1,0,1), and (0,1,1) generate F3.

A:

Q: Find a vector orthogonal to both (-4,5, 0) and to (0, 5, 4) of the form (1,

A:

Q: Show that the vectors are orthogonal.

A: Given : 3,6 and 4,-2

Q: The vectors (-1, 2, – 1) and (2, –4, 2) are parallel and not orthogonal. True False

A:

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.