Which of the following subsets are linearly independent ? B = {(2,1), (-3,-2), (9, 11)} %3D B2 = {(4, –1), (5, 3)} %3D B3 = {(0,0,0,0)} |3D B4 = {(1,2, –3, 4)}

Q: Question (3): Determine whether the set S is linearly independent or linearly dependent a) S= {(2,…

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Q: If A ∈ R^n×n is invertible, then columns of A^−1 are linearly independent. Explain why.

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Q: и, %3 (1,3,5) и, — (0,-1,2) и, — (2,5,12)

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Q: What condition must a, b, c & d satisfy so that matrices are linearly dependent? [::] 1 2 2 3 a b…

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Q: Let w = ( -1, -4, -9). By appropriate use of the augmented matrix and elementary row operations…

A: We have to check that w is linear combination of given vectors or not.

Q: Find the sum of components (X, + x,2), x,²) ) (2) of second linear yiskem, using the initial…

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Q: Express the linear function as F(x) = CX for some matrix C. f(x1,x2,x3,x4) = (5x3 - x1, 2x3 + x4,…

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Q: -4 -3 u = -3 = w = -3 18 8 + k are linearly independent if and only if k +

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Q: Determine: If S = {X2,1 + X2} is linearly independent or dependent.

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Q: Let x1 = (1/2, 1/2, 1/2, 1/2), x2 = (-2, –1, –4, –1), X3 = (1,2, –1, 1), x4 = (1, 1, 1, 0). (a) By…

A: Given that x1=12,12,12,12,x2=-2,-1,-4,-1,x3=1,2,-1,1,x4=1,1,1,0. Note: send part (b) and part (c)…

Q: Give the value(s) of a for which the columns in the matrix 9 6 -6+a A= 6 12 -6 -6+a -6 are linearly…

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Q: If the set {(1,2, 1), (0,1, 1), (1, -3, A)} is linearly independent, then (A) A = -4 %3D (B) A + 4…

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Q: Suppose that the matrix X is partitioned as [ G T] [: а b Then X"X = where d

A: Suppose that the matrix X is partitioned as [ G  T ].

Q: The following augmented matrix correspond to a linear system in three variables, 25 x, y and z, 01-3…

A: We have to solve the given system of linear equations. A system of linear equations can be written…

Q: Find the values of for which :=,0) and": =(a.1) are 4a-4 linearly independent in *".

A: To find the values of a for which the below vectors are linearly independent in R2. v1=4a−4, av2=a,…

Q: 3. Find the matrix X, such that XC - 2C = DXC satisfies. 3 4 4 4 1 C = 1 2 1 D = 1 0-2 4 1 -1 -3

A: Since there are multiple questions, we are solving the first question. Please post the questions…

Q: Given is the following set of equations X1 4.8 18 10.8 38.4 X2 7 14.68 39.4 X3 where the coefficient…

A: Introduction: The motivation for a LU decomposition stems from the observation that systems of…

Q: 1.Determine, if S is linearly independent or dependent. Let S= = {(6, 2, 1),(−1, 3, 2)}. 2.…

A: A set of vectors A={v1, v2......vn} is said to linearly independent if there exist scalars such that…

Q: 2 -1 0 2 4 4 3 1 A -1 8 -12 A -2 2 -2 6 4 1 1 ||

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Q: 3. Check whether (2, 4) and (1, 2) are linearly dependent or not?

A: Linearly department vectors

Q: 5) Is {(1,4, –6), (1,5, 8), (2, 1, 1), (0, 1,0)} a linearly independent subset of R3? Justify your…

A: Consider the set of Vectors S={(1,4,6),(1,5,8),(2,1,1),(0,1,0)} Our objective is to determine…

Q: Let B = {b1, b2} and C {C1, C2} be R2. Produce the change-of-coordinate matrix from B to C and from…

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Q: 3 If a + 1 is linearly dependent in R', find a. 2 a + 2

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Q: Q/use Gaussian Elimination method to find the value of a, aa2 a3? ба, + (155)а, + (5525)а, +…

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Q: If Pis the projection matrix onto the line through (C) m« (;) and then I – P projects onto the line…

A: Option B will be the right answer.

Q: To determine whether a set of n vectors from R" is independent, we can form a matrix A whose columns…

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Q: If Ax = Bx for some nonzero vector x, then the matrices A and B must be equal.

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Q: Let -3 -4 4 A = -3 -4 4 -4 -3 Find an orthogonal matrix P and a diagonal matrix D such that D =…

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Q: Given data set (-1,2), (0,1), (2,3), (3,5), what is the associated matrix A that helps finding the…

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Q: Let B = {b1,b2} and C = {c1, C2} be R². Produce the change-of-coordinate matrix from B to C and from…

A: The change of basis matrix form B to C (or from the basis B to the basis C ) and C to B where B and…

Q: Suppose a, = (1 -1 1 1) 5. a, = (1 0 1 0)" a, = (1 1 1 1)'a, = (3 2 3 0)" · Please find out whether…

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Q: Let A, B be two matrices with linearly independent columns. If Col(A) = Col(B) then A(AT A)-1 AT =…

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Q: Find the SUM for mean of the matrix F * ? F= 1 1 1 2 2 2 2 3 3 3 3 1,

A: In order to follow sum for mean of the matrix.  First find the mean for the matrix then take sum for…

Q: Which of the following must be true? If Mis a linearly dependent set, then every vector in Mis a…

A: In first option insted of every if we have at least one  then it is true . For option second insted…

Q: Which matrix is of the reduced echelon form? Oa. (1 2 04 0 0 2 7 Ob. 1 2 5 0 13-7 10 1 0 0 0 01 0…

A: To find the reduced echelon form of given matrices.

Q: Determine whether or not the following sets S of 2 x 2 matrices are linearly independent. {(; 7) (,…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: Q5) Determine whether the following matrices from M form a linearly independent set 2,2 A = [; ]),8…

A: Given set of matrices are linearly dependent

Q: Does the matrix define a linear function T that is one-to-one and onto? -3 0 A = 0 3 O Yes No

A: To determine: The given matrix define a linear function T that is one-one and onto. Given…

Q: If the set {(1, 2, 1), (0, 1, 1), (1,–1, A)} is linearly independent, then (A) A# -2 (B) A # 2 (C) A…

A: The objective is to find the correct option.

Q: Which figure of the followings represents trajectory behaviors for the system a'=

A: Step:-1 Given system is x' =01-2-3 xx'= A x For solution, we'll find Eigen values and Eigen vectors…

Q: If the set {(1,2, 1), (0,1, 1), (1, –2, A)} is linearly independent, then (A) A#3 (B) A # -3 (C) A =…

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Q: Let -3 -4 4 A = -4 -3 -4 -4 -3 Find an orthogonal matrix P and a diagonal matrix D such that D =…

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Q: The following augmented matrices represent different linear systems In x, y, z Which of the linear…

A: The augmented matrices are given then which linear system has unique solution.

Q: S={(1,0,2),(1,1,1),(−1,15)} is linearly independent. True or false?

A: S=1, 0, 2, 1, 1, 1, -1, 1, 5 Now, 1 1-10 1  12 1  5=15-1-10-2-10-2=4+2+2=8≠0

Q: Determine whether the following subsets of Mat2,2(R) are linearly independent. If not, write one of…

A: Given the subsets of Mat2,2ℝ are 1.   0111 , 1011 , 1101 , 1110  2.   -11-22 , 3011 , 02-31 , -10-17…

Q: If the set {(1,2, 1), (0, 1, 1), (1,-2, A)} is linearly independent, then (A)入¥3 (B) A# -3 (C) A =-3…

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Q: Given matrix A = (2 /3 |−1/5) and that h(T) = T2 − 2T − 7, find h(T).

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Q: ) Determine whether or not the rows of A are linearly indepen O independent O dependent Let the…

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Q: Consider the following two data vectors: A = [3,7,11] B=[3,2,1] Calculate the covariance matrix of…

A: The given two vectors are: A = [3,7,11] ; B=[3,2,1]. Need to find the covariance matrix of these…

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.