[1 3 5 0 71 Given A = |0 0 0 1 2, li 3 5 1 9] (a) Find the reduced row echelon form R of A. (b) Find the dimensions and the basis of the four subspaces of R.

Q: 1. Find a basis for the vector subspace of 2 x 3 matrices given by а 6 c V := { : a + b+ c= 0, a = c…

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Q: 2. Let S be the subspace of R5 spanned by x = (1, , (a) Find a basis for S- (b) Give a geometrical…

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Q: The sets B={[1 2 2 1]T;  [1 0 2 0]T;  [2 0 4 -3]T} and B'={[0 2 0 1]T;  [2 1 4 -1]T;  [1 2 2n 4]T}…

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Q: Given: a = [1 1 0 -1] b = [ 0 1 2 1] c = [ 1 0 1 -1] d = [ 1 1 -6 -3] e= [ -1 -5 1 0] Suppose, x =…

A: The basis is a set of linearly independent vectors that spans the given vector space. A basis is to…

Q: Let -2.5 * = -4 and j = 7 -6 Use the Gram-Schmidt process to determine an orthonormal basis for the…

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Q: -3 -10 1.5 -2 18.5 ミ= ÿ = -5 -9 7 Use the Gram-Schmidt process to determine an orthonormal basis for…

A: Given vectors are x→=−3−1−40, y→=−10−2−51 and z→=1.518.5−97. We have to find an orthonormal basis…

Q: 5. Consider the vectors in R³, and let W be the subspace Span{x1,x2}. (a) Find an orthogonal basis…

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Q: Use Theorem 5.2.1 to determine which of the following are subspaces of R3. (a) all vectors of the…

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Q: -2 Find the orthogonal projection ŷ of y = 3 onto the subspace 2 -2 W = Span { u , U2 Ex: 1.23 : ||

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Q: 10. Find a basis for the subspace spanned by the given vectors. What is the dimension of the…

A: Given vectors  1-32-4,-39-612,2-142,-45-37 we have to find    (a) Basis for the subspace spanned by…

Q: 5. (а) Show that the formula ((: :) (; 3)) = xã + 2yỹ+ zž + 2wũ gives M2x2(R) the structure of an…

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Q: a Let M = . -b a,b,c e R},N x, y e R} be two subspaces of M2x2. Find the basis for M, N and MON.

A: We will find the bases of M and N. Then we will find the intersection of their basis vectors, which…

Q: 1 1 −1 2 1 2 1 Let A = and T the corresponding linear trans- 1 0 2 1 1 −1 2 3 formation of R4, find…

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Q: Find a basis for the given subspace of R’, and state its dimension for the plane 4 x - 2 y + 5 z = 0…

A: Solution:-

Q: Use Theorem 5.2.1 to determine which of the following are subspaces of p3. (a) all vectors of the…

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Q: [1 3 5 0 9 0 0 0 1 8 1 3 50 9 Find the four subspace for the given matrices. A

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Q: Find a basis for the given subspace of R , and state its dimension for the plane 2 x - 4 y+ 5 z = 0.…

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Q: 3 1 Show that the null space of A is a 02 subspace of R³. Which subspace can you obtain by the…

A: It is given that,  A = 13-1024 We have to show that the null space of A is a subspace of ℝ3 and to…

Q: The given vectors form a basis for a subspace W of R³. Apply the Gram-Schmidt Process to obtain an…

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Q: 1. Let W = {( 2).a+ 2d = 0}. Show that W is a subspace of the set of all 2 x 2 matrices and find its…

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Q: Find bases for the four fundamental subspaces of the matrix A. 1 3 4 A = 0 7 0 N(A)-basis N(AT) =…

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Q: The solution space of the homogeneous linear system 0 0 Ax = 0, where A 1 2 0 is a subspace of R³.…

A: Given the homogeneous linear  system  Ax=0 , where  A=200120-352 Let   x=x1x2x3         x1 , x2 ,…

Q: 3.8 Using the Gram-Schmidt method, turn the basis B = (b1, b2) of a two- dimensional subspace U C R…

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Q: A matrix A and its reduced row echelon form are given below. [1 0 8/5] 0 1 1/5 0 0 0 0 [1 2 2] 2 4 4…

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Q: [1 1 07 Let matric A be a square hermitian matrix= |1 0 0 Lo 1 Use Gram-Schmidt process to find the…

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Q: Find bases for the four fundamental subspaces of the matrix A. 157 A = 0 2 0 N(A)-basis N(AT) =…

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Q: Find a basis for the following subspace of Rª over R: 3 1 4 7 span 10 11 13 What is the dimension of…

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Q: 4. Find a basis and the dimension of the subspace W of V = M22(R) spanned by %3D -5 2 -4 A = B = C =…

A: Given:          V = M2 × 2(ℝ) spanned by A = 1-5-42 ; B = 11-15 ; C = 2-4-57 and D = 1-7-51   To…

Q: -3 Find the orthogonal projection ŷ of y = -1 onto the subspace -2 5 W = Span { u1 = -5 u2 = -3 Ex:…

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Q: -5 -1 and v = 9 Let vi = Let W be the subspace spannd by the u's. Use the -9 3 Gram-Schmidt process…

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Q: 1. Let v, = (43 2 1), v, = (-2 0 -1 0), v3 = (0 3 0 1) a) Find the subspace of R* spanned by these…

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Q: Find bases for the four fundamental subspaces of the matrix A. 15 4 A = 0 2 0 N(A)-basis N(AT) =…

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Q: Find a basis for the given subspace of R', and state its dimension for the plane 4x-2y+5z 0. V1 = 1…

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Q: Let 3 ГО.5 and j = |-4 [0.5] Use the Gram-Schmidt process to determine an orthonormal basis for the…

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Q: [1 2 2 4 6 2. Find a basis for the four subspaces of A = |1 2 3 6 9 0 0 1 2 3

A: Given: A=122461236900123             ~122460012300123    R2⇒R2-R1             ~122460012300000…

Q: -3 x = -4 and y Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of…

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Q: Find a basis of a subspace U in R given by a system: I1 - T2 + 2r3+T1 T1- 12 + 313 + 2r, 0

A: (a) Given the system x1-x2+2x3+x4=0x1-x2+3x3+2x4=0 which describes the subspace U∈ℝ4.   To find the…

Q: Find bases for the four fundamental subspaces of the matrix A. 189 A = 0 30 N(A)-basis N(AT) = %3D…

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Q: Find the bases for Col A and Nul A, and then state the dimension of these subspaces for the matrix A…

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Q: Find a basis for the subspace and state the dimension. p– 2q 2р-5r :P,q,r e R а. -2q +2r -Зр+ 6r| 1…

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Q: 6. a. Give a basis for the orthogonal complement of the subspace V C R' given by V = {x € R* : xị…

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Q: 8. Let S = LE M2x2 : A = -1 (a) Given that S is a subspace of M2x2, find a basis for it. (b) Is it…

A: This belong to linear algebra.we first find the type of matrix belong to s then find the basis for…

Q: Find the basis for the given subspace of R°, and state its dimensions for the plane 2x – 4y +5z =0.…

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Q: Let P2 be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

A: We will find out the required solution.

Q: Let 3 -2 -2 and j -4 -4 -14 4 Use the Gram-Schmidt process to determine an orthonormal basis for the…

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Q: 6. Let S be the subspace of R3 that consists of all solutions to the equation x+5y−z = 0.Find a…

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Q: 1 1 11. Find a basis for the subspace of R4 spanned by u1 = U2 = U3 and -3 1 1 1 U4 =

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Q: 6. (a) Find a basis for the subspace of R' spanned by 1 4 7 -5 7 4 w = 4 -5 (b) Using part (a),…

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Q: Find bases for the four fundamental subspaces of the matrix A. 15 1] A = 0 2 0 N(A)-basis N(AT) =…

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Q: -3 -10 -2 -2 and let W the subspace of R4 spanned by ű and v. Find a basis of W+, the orthogonal…

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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.