[1 2 -1 4 ol 21 Q. No. 02 Let A= |3 5 li 1 a) Find the basis of row space and null space of A. b) Rank(A). c) Number of free parameters in the solution of Ax = 0.

Q: Find a basis of ker T. T: M22 → 1 M22; T( x ) = AX, where A = 0 0 O[1 0 0 1 0 1 1 0 1 0 1 0 0 -1 0…

A: The transformation T:M22→M22; T(x)=AX, where A=1100. We have to find the basis of kerT.

Q: -10 4 Let {uj = | 3 u2 30 u3 be a basis for R. Use the Gram-Schmidt process to 20 find an orthogonal…

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Q: 59. In R4, given 2 nullspaces 1 2 00 1 V : |-1 0 -1 m 0- Find m such that dim(U n V) is max. Find…

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Q: 2. Consider the following matrix and vector 1 2 3 4 A = 2 2 6 8 b = Find the particular solution and…

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Q: 9. (Strang 4.1.22) If P is the plane of vectors in R' satisfying r1+x2+ x3 + x4 = 0, find a basis…

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Q: -2 Let y = what are the expansion coefficients of y in the basis {vo, V1, V2 , v3 } you found in the…

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Q: -6 Express the general solution of Ax =b where A = and 6 -12 -6 as x = x, + cx„ where x, is the row…

A: Given: Matrix A=3-66-12 and B=-6-12. The objective is to express the general solution of Ax=b.

Q: Find the coordinates in R° of x = (13, 26, 39) relative to the orthonormal basis 12 5 12 B = 13 13…

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Q: 8. Let x and y be vectors in 3-space, and suppose u is orthogonal to both x and y. Prove that u is…

A: Let x and y be vectors in 3-space and suppose u is orthogonal to both x and y  This implies  < x,…

Q: Is this the basis? What is the rank of A?

A: According to the given information, it is required to find the basis and rank of matrix A. The…

Q: After applying the Gram-Schmidt Orthonormalization Process to the basis 8. B = we get the basis a B'…

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Q: (a) Find the basis for the solution space of I1 +a2 - a3 = 0, -2.r1 - 12 + 5rz = 0, -21 + 4r3 = 0…

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Q: 0 10 2-1 10-1 1 O Find a basis of the row space of A = by reducing A to reduced echelon form. 0 1 0…

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Q: Suppose A E R4×3 has the following QR factorization A QR V2 -V2 [1 0 1 0 0 0 0 -1 1 1 1 -1 R = 1…

A: We will first find the matrix A using the QR factorization given.…

Q: Find the basis of the null space of A. 3 1 1 2 A = 4 1 2 1 1 –1 1 1 1 -1 [2 2 1 2 1 2

A: Step 1: Transform the matrix to the reduced row echelon form

Q: EX ample (12.1) Find the Singular Value De composiion of A= 0 4 3 4 00 3 00 Solution: FInd Q2…

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Q: 1 0 1 Find a basis for the null space of the matrix A = 0 0 0 9 0 9

A: Basis of null space is the solution of AX=0.

Q: (a) Find the basis for the solution space of #i + x2 – a3 = 0, -2.x1 – x2 + 5æz = 0, -#1 + 4.r3 = 0…

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Q: 1//18 1/V2 |-2/3 4/V18 is a orthonormal basis of R³. Using the Determine if 1/3 1//18 1//2 -2/3 1…

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Q: 6. Determine the basis for the null space of -2x + 2y + 2z] a) 3x + 5y + z 2y + z х — 2у — z b) -x +…

A: Introduction: Null Space, like Row and Column Space, is a simple area in a matrix, including all…

Q: IS Suppose that z = 0 is a regular singular point of the ODE az(x)y"+a1(x)y' +ao(x)y =0 and that ri…

A: We have to write solutions set for the given differential equation.

Q: [ 4 -1 Find a basis for the null space of A = - 20 {le Ex: 1

A: If x belongs to null space of a matrix A then Ax is equal to zero.

Q: (4) 10. Let H = {r+2x2, 1+ ka?, k + (2k + 3)r2} (a) For what value(s) of k is H linearly dependent?…

A: This belong to linear algebra.we check linear independence for the given vectors and find k so that…

Q: 4. A = 3 -6 -12 -3 -6 -9 -3 Find an orthonormal basis of the kernel of A.

A: Note: We know that the kernel of a matrix A is the set of solutions of the corresponding homogeneous…

Q: Please give correct answer

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Q: What is [A]B, the coordinates of A = | 3 with respect to the standard 8 1 0 0 1 basis B of R2x2? 0 0…

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Q: 3. (a) Compute the matrix multiplication 1 A −2 1 −3 ] (b) Write down the solutions of the…

A: see my solution

Q: Find the basis for the solution space of I1 + x2 – 13 = (0, -2r1 – 12 + 5r3 = 0, -*1 + 4r3 = 0 and…

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Q: 20. Let {u1, uz) be the orthonormal basis obtained by applying the Gram-Schmidt procedure to the…

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Q: -7 -7 The orthogonal basis produced using the Gram-Schmidt process for W is (Use a comma to separate…

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Q: 10 40 5 5 5 2 1 3 3 3 a- a basis for the row space ofA b- a basis for the column space of A c- a…

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Q: 4.) Find (a) a basis for and (b) the dimension of the solution space of the homogeneous equations…

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Q: 1 A = 2 1 1 3 Find an orthonormal basis of the image of A.

A: A=-11-211-3 Orthonormal basis of A using the Gram Schmidt process. v1=-1-21, v2=11-3…

Q: 11. Find a basis for the set of vectors in R³ in the plane x + 2y + z = 0. [Hint: Think of the…

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Q: 4.) Find (a) a basis for and (b) the dimension of the solution space of the homogeneous equations…

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Q: 2 1. Find a basis of the null space of the matrix B -2 -2 -4

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Q: - --- Let B = Is Ba basis ofR ? Justify and x = %3D 2 3 3 your answer. If yes, compute xR [x]

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Q: Lemma 2.8 B is a basis of T iff

A: To prove that Β is a basis of Τ iff ∀Ο∈Τ ∃ Β0⊂Β: Ο=∪ ΒΟ

Q: [1 2 4' 2 – 4 0 1 0 – 2 0 1 3 A. (Hint: Need to apply row reduction to AT to identify the lin.…

A: Given                           A=1242-4010-2013 Determine a basic for the row space by choosing…

Q: 7.C.1: Prove or give a counterexample: If TE£(V) is self-adjoint and there exists an orthonormal…

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Q: 10. The solution set to the equation Ax = b is 1+t1 2 - t t + u :t, ueR} when b %3D L2t· - u a) How…

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Q: 1 1 1 1 2 3 A = 1 3 3 4 4 -2 -2 1 -4 | Find an orthonormal basis of the row space R(A) of A.

A: Consider the matrix A=1112122321332244-2-21-4. The objective is to compute the orthonormal basis of…

Q: 1.2 Find a basis B for the domain of I Suh that the mahix for ī alative to Bis iagend. Hogand. T:…

A: We have to Find a basis B for the domain of T such that the matrix for T relative to B is diagonal.

Q: Let P2 be the polynomials of degree no more than 2. Is {x2+x+1,2x+1,3x2+1} a basis for P2 ?

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Q: (a) Give a basis for the null space of A. 12 1 13 (b) It turns out that A- 1 -1. Give a…

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Q: a b 1) Let T cla + 2b + 1c + 3d + (-11) e+ (-la+ (-1) b + (-2) c + Od + 7e) x. d to Then a basis for…

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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.