3. Let vi = [1, -2,3], v2 = [-1,–4,5], and v3 = [5,-1,3] be vectors in R³. a) Use determinant to show that v1, v2, and v3 are linearly dependent. b) Use Gauss-Jordan elimination to write Vị as linear combination of v2 and v3.

Q: Use the definition of Ax to write the vector equation as a matrix equation. 3 - 4 4 9 - 3 + X3 3 %3D…

A: We will do this by using definition of augmented matrix

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A:

Q: 31. The vector perpendici:!at to both 3i –-6j – 4k and -3i + 2j + 2k is A A -4i + 6j + 12k B - 4i +…

A: Cross product

Q: D. Prove i [- 2,5, 1], 7 = [2,1, – 1] and w [- 6,0, – 12] are orthogonal. %3D

A:

Q: Suppose that 60% of the people who own a GM car buy a GM car for their next vehicle. Also, suppose…

A:

Q: Let U be a square matrix such that UTU = I.  Prove that the determinant U = + 1.

A:

Q: z= 5x, + 12x2 + 4 x, S.t X, + 2x2 + X, s 8 2 x, - X2 + Xạ = 8 where x,, X2, Xs 20

A: For a Minimization Problem, The constraints must be in the form≥ in the standard Primal Form.…

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A:

Q: Let A and B be nxn inversible matrix. Prove that AB is invertible and (AB)-1=  B-1A-1.

A: Let A and B be n x n invertible matrices, with inverses A-1 and B-1, respectively.

Q: Suppose that a 3×3 matrix A has three columns C1, C2, C3 which span the plane given by x + 2y – 5z =…

A:

Q: 2. (a) Express -2+t+t +r' as a linear combination of 1-t, 1+r, and 1+1- or show that it cannot be…

A: We have to write in the linear combination.

Q: as a linear combination of x = 7 4 and y = -3 Express the vector u -2

A: NOTE: Refresh your page if you can't see any equations. . write both vectors x and y in the matrix…

Q: .

A:

Q: Show that the three points (x1, y1), (x2, y2), and (x3, y3) in a plane are collinear if and only if…

A:

Q: Let A be a 3 × 3 matrix and let x1, x2, x3 be vectors in R3. Show that if the vectors y1 = Ax1, y2 =…

A: Let A be a 3 × 3 matrix.

Q: 4. Prove: If b is a non-zero vector, and x and x are both solutions to the matrix equation AX =6,…

A:

Q: Consider four row vectors u, u, w, z of size 1 x n each and let a, bER Then. by multilinearity of…

A: The given statement is

Q: at vectors （c1 - a1, c2 - a2）and （b1-a1,b2-a2）are linearly depend

A:

Q: Denote the column vectors of the matrix 11,922.. , ann +] True, false, or uncertain: a; is…

A:

Q: Find the change of basis matrix from B2 to B1. -4 B1 = , B2 B2 = 2

A: The change of basis matrix C from B2 to B1( or from the basis B2 to the basis B1 ): β1=-142,231  and…

Q: Construct a 3 x3 nonzero matrix A such that the vector is a solution of Ax = 0. 1 LA =

A: x=-1-1  1 Now let A=abcdefghi be the required vector. Then, Ax=0⇒abcdefghi-1-1  1=000⇒-a-b+c-d-e+f…

Q: Find the change of basis matrix from B1 to B2. -1 2

A:

Q: 1 3 Let the inner product in R be generated by the matrix 4 = -1 2 Calculate the inner product of…

A:

Q: If a 4 x 4 matrix A with rows v1, v2, V3, and v4 has determinant det A = 4, %3D 4v1 + 5v2 7v1 + 9v2…

A: See the detailed solution below.

Q: Let the matrices Ho, H, Ha 1x1 M어ni x [1]. be defined ... the He=L He-I vector of length n-2" can be…

A:

Q: Show that if C is a matrix whose columns are the components (x1, y1) and (x2, y2) of two…

A: Concept: A branch of mathematics which deals with symbols and the rules for manipulating those…

Q: When V is spanned by {v1, v2, . . . , vk} and one of these vectors can be written as a linear…

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A:

Q: (c) 0 is neither diagonalizable nor

A:

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: If {u1, u2, U3, ... set of vectors in R" and the matrix U has columns u1, ..., Uk, then U'U is the…

A:

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A:

Q: Show that u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2) are linearly dependent show all working and explain…

A: Given :u1 =(2,1,1) u2= (-2,2,1) u3= (1,-1,-2)

Q: Solve the following linear system of equations using Cramer's Rule

A: We have to solve the following linear system of equations using Cramer's Rule.

Q: Construct a 3 x 3 nonzero matrix A such that the vector is a solution of Ax = 0.

A: Given conditionAx = 0          .................(1)x = 111 is a solution to Ax=0,Let matrix A be - A…

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A:

Q: TRUE/FALSE Assume that all the given matrices are n × n. If A and B are row equivalent matrices,…

A: Given: All the given matrices are n × n. A and B are row equivalent matrices.

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

A: I have checked one by one option wise

Q: Express the quadratic form as v Av, where A is a symmetric matrix. x² + 3y² + 5z² - 4xy+3yz + 10xz

A:

Q: Give an example of a 2 x 3 matrix A that is in RREF and whose solutions to 2 -(-) 4 Ax = 0 is…

A: Introduction: Systems of linear equations can be solved using a type of matrix called reduced row…

Q: Find the matrix P that multiplies (x, y, z) to give (y, z, x). Find the matrix Q that multiplies (y,…

A: The matrix “P” will be, P=010001100  if multiplies (x,y,z) to give (y,z,x) Explanation:…

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A: You asked to solve only (a). (a) Solution:  We will explain here how to compute the determinant of…

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A: Let's suppose we have a linear relation:…

Q: Write down anxn matrix A such that Cond(A) =1, but determinant(A) → 0 as n → ∞.

A: claim- write down a n×n matrix A such that CondA =1 but determinantA→0 as n→∞ let the matrix be…

Q: 20. Can every vector in R* be written as a linear combination of the columns of the matrix B above?…

A:

Q: let A be an mxn matrix and v and w vectors in Rn. If v and w were both solutions to Ax=0, show that…

A:

Q: Suppose you solved a second-order equation by rewriting it as a system and found two scalar…

A:

Q: Use induction to prove that the determinant of a diagonal matrix is the product of all the entries…

A: Consider a diagonal matrix An, An=a10⋯00a2⋯0⋮⋮00⋯an Let Pn is is determinant of diagonal matrix An…

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.