The dimension of the subspace W = {A E R™Xn: A is diagonal} is 2. balg j

Q: Which of the following is the dimension of the subspace b W = :a = b - c and a, b, c,d eRC R* ? (a)…

A:

Q: Determine whether or not the given set W is a subspace. A W = {T E R" | AT = 23 – BE }, where A, B…

A:

Q: A vector y in Rn can also be viewed as an n × 1matrix Y = (y). Show that ||Y||2 = ||y||2

A:

Q: Which of the following is not a subspace of R? Select one: O A. W={X: I1 B W= {X:1= T, of I, = O…

A:

Q: Let v₁ = (2,1,0,−1), v2 = (0, 1, 2, 1), and b = (1, 8, –1, −7). Let W be the subspace or R4 spanned…

A:

Q: 2. Let а — lb +c а S = {[a – b ,b,c € R a a. Show that S is a subspace of M2x2. 31 -2 31 5 b. Is |…

A:

Q: Construct any 2 by 3 matrix of rank one. Copy Figure 4.2 and put one vector in each subspace (and…

A: First we have to construct a 2x3 matrix of rank 1. then find the vector in the subspace (row space…

Q: Determine whether the set of all matrices of the form (:: ;). a bc 1o), where a+e 0, and b +d+f 0,…

A: Given: abcdef , a+c=0, b+d+f=0

Q: Find the nullspace of the matrix

A: By definition , nullspace of a matrix A is the collection of all vectors x such that Ax=0 Given…

Q: 2. Determine whether W = {a + br + cr?; a, b, c € R, a · b.c= 0} is a subspace of P2.

A:

Q: Let W be the set of all vectors of the form a b where a - C = 4 and b - C = - 5. Lc Then, W is a…

A: Given: W=abc|ac=4, bc=-5 To prove W is subspace or not.

Q: 10. Is 2 = {(x, y,z)| x=2 y & z=1} a subspace of R³?

A:

Q: find the components of the vector −→P Q. P = (1, 0, 1), Q = (2, 1, 0)

A: Given  P=<1,0,1>Q=<2,1,0> The component form of a vector is the ordered pair that…

Q: Only use the definition of subspaces, determine whether U = {(-a,–2B+a,a – 3,)| a ER and ß E R} is a…

A:

Q: Q3 shew that W2 = subspace of R2 is a

A: To show any subset of vector space is a subspace , prove the following condition : Set is closed…

Q: Find the dimension of the subspace U={[a+c, b+c, a+2c+b] | a, b, c in R} Select one: a. 2 b. 4 c. 1…

A: We have given a subspace ,  U = a + c , b + c , a + 2c + b / a , b , c ∈ ℝ We need to find dimension…

Q: 2.6. Find the distance from a vector (1, 2, 3, 4) to the subspace spanned by the vectors v₁ = (1,-1,…

A:

Q: Draw Figure 4.2 to show each subspace correctly for A = and B = 36 3

A: Given matrix is .Here A is a linear map from  to  . So, we get n=m=2.Find the row space of A:Find…

Q: Q2. Let V = {(a, b, c, d) : b + 2c + d = 0} and W = {(a,b, c, d) : a + 2b = 0, c = 5d} be two…

A:

Q: 1. Determine whether W ER is a subspace of M. %3D b 2a

A: We have to determine whether W is a subspace of M22.   According top our guidelines we can solve…

Q: Let W be a subspace spanned by the u's, an

A: Given, W be a subspace spanned by u's, and write y as the sum of a vector in W and a vector…

Q: A base of the subspace W={ (a, b, c); a-2b+c=0} is:

A: According to the question,

Q: Determine whether the following sets are subspaces of R³. Realize number 4 as the span of a…

A:

Q: Show that W = {a + bx² € P₂|a, b = R} is a subspace of P2.

A: The solution is given as

Q: The vector x is in a subspace H with a basis ß = {b1,b2}. Find the ß-coordinate vector of x 9) b₁ =…

A: Introduction: To find the β-coordinates of the given vector corresponding to the the given basis…

Q: Determine whether or not W = {[a, a?, b] | a and b are real numbers} is a subspace of R³. Justify…

A: See the detailed solution below.

Q: Find the dimension of the subspace of all vectors in R5 whose first and third entries are equal. The…

A:

Q: The set of all vectors in R squared  that satisfy 3x+4y=1 is a subspace of R squared . True False

A: 1. The set of all vectors in R squared that satisfy  3x+4y=1  is not a subspace of R squared.  i.e.…

Q: Determine if set S is a subspace or not S = {(a,0₁0) € R² } Ⓒ @ 3 S = {(₁₁ 6₂c) | b=a+c} in R (3) S…

A:

Q: 2 Find bases and dimensions for the four subspaces associated with A and B: A = 1 2 4 and B= = 1 24…

A: We will find the bases and dimensions.

Q: Solve the following questions: Q1) Check whether the set W = {(2a + 5b, –a + b, 3a + 4b); a, b are…

A:

Q: The subset in the form [3]. Select one: O TER and y = -x. O None of these O r = -y and y ≤ 0. Or#0…

A:

Q: Choose all that apply for the set S2 e R : 3x1 - x2+ 5x3 12 x3 O S2contains the zero vector. O Szis…

A: The given set is                                S2=x1x2x3∈ℝ3 : 3x1-x2+5x3=12

Q: What is the dimension of the subspace U = -{(8 3 2 6 a b-b C 0 C c): a,b,c : a, b, c ER of M2x4 (R)?…

A:

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.