Given two subspaces A = {(a,b,0): a,b e R} and B = {(c,0, d) : c,d e R} of R°. |3| O A. R' is equal to the direct sum A B O B. R is equal to the direct sum A Bonly if c = 0 O C. R is equal to the direct sum A O B if either a = O or c = 0 O D. None of the listed alternatives are true. O E. R is equal to the direct sum A B only if a O and c = 0

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

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

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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…

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Q: Let u = (9,3,-3), v = (0,2,-5), and w = (6,5,4). Compute v X w. vxW=(

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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: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: State the dimension of the following subspace, The solution space {(a,b,c): a-3b+c=0, b-2c=0,…

A: We have to find the dimension of the subspace.

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

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

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

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Q: Write v (2,5, –4,0) as a linear combination of uz = (1,3,2, 1); U2 (2, — 2, -5,4); из %3D (2,…

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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: Let-{ », :x, y, a, b e R and x - a = y – b}.Is W a subspace?

A: We will use the one step test for vector subspace to check if W is a subspace or not. We know that…

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

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Q: 19. Prove that the set of all vectors in R³that satisfy the equation x₁ = 3x2, is a subspace.

A: (.)  Let set  'S'  is given by ,        S=x1,x2,x3∈ℝ3  :  x1=3x2 or   S= x1,x2,x3∈ℝ3 :  x1-3x2=0…

Q: Find the closest point to y in the subspace W spanned by u₁ and ₂. y = 19, Un 28 国 26 20 -2 -26…

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Q: Let vi = (-9,9, 6). v2 = (2, 6, 4). v3 = (4,0,0) in Rº. Find a nontrivial linear relation among…

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Q: The following question is from linear algebra : Factors the vector (6, -5, -1)t into three…

A: Given a vector  which s to be broken into three components .The component  depends on ,…

Q: 10. The set of vectors: [0 1-3 -1], (1 01 1] is linearly independent. Answer: yes or no

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Q: Which of the following sets are subspaces of R³: W1 = {(x1, x2, X3) : x3 = 2x1 – 4x2}; W2 = {(x1,X2,…

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Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: The four subspaces are Nullspace, Column space, Row space, and Null space

A: Please give a helpful review after seeing the quality of solution provided. Each and every step is…

Q: Let a = (1, – 5, 3) and b = ( – 5, 3, k). | Find k so that a and b will be orthogonal. k =

A: a→=1,-5,3b→=-5,3,k To find: value of k for which both will be orthogonal.

Q: Find a linear map T that maps [0, 1] × [0, 1] to the parallelogram P in the xy-plane spanned by the…

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Q: Q2. In the vector space V = R°, if we take a set: S = {(4,5, 6), (k, 5, 1), (4, 3, 2)} %3D Find the…

A: In the vector space V = R3 , if we take a set S = { ( 4, 5, 6 ), ( k, 5, 1 ), ( 4, 3, 2 ) }. Then,…

Q: 3. Is the set of all vectors (x, y) in R2 with the usual addition and scalar multiplication, a…

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Q: Find a set of vectors that spans the subspace W CV of solutions to the following linear systems. 1.…

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Q: 4. Show that the vectors v1, v2, and v3 are linearly dependent, where Vị = V2 = and v3 =

A: If we have a set of vectors v1, v2, v3, ..., vn, then they are said to be linearly dependent if…

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

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Q: If u = [3, - 1] and v = [1,4],compute and draw u + v.

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Q: X b) Let T 10 Find the Kernel of T. Write down the range of T as a span of independent 5x vectors.…

A: Obtain Kernel of T as follows.

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.