1 -1 4. Find a vector v for which 2 1 is a basis of R³. 3 1 5. Find a vector v for which is not a basis of R³.

Q: near Methods

A: Given, x1x2˙=14-4510x1x2+4t3e12t2 cos4t-4 sin4t5 cos4t+8t7e12t4 cos4t+2 sin4t5 sin4t The eigen…

Q: 1. Let S = 3 -6 (a) Is S a spanning set of R3? (b) Are the vectors in S linearly independent? 2. Let…

A: The following questions has been solved below.

Q: Let V be a vector space with a basis B = {b₁, What is the B-matrix for the identity transformation…

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Q: 10 -7 Let u = and v = Compute u • v, v · v, ||u|| and find the dis- 13 16 tance between u and v.

A: Given  u=10-7135 and v=-44316

Q: Given u and v, find compu. u = [−1, 6, -7] v = [2,-4, -8] compu Ex: 1.234 -

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Q: 7. Use an adjoint matrix to solve the linear system. 2r + 3y – 5z = 22 y+ 3z = -8 2z = -6

A: The given system of linear equation is 2x+3y+5z=22, y+3z=-8 and 2z=-6. Express the above system of…

Q: Use paper and pencil to identify the redundant vectors. 4 3. 0. 0.

A: Definition : Redundant vector in a set is a vector which can be written as linear combination of…

Q: 2. Find the general solution of the system of differen- tial equations d X = dt + 4t³e4 / sin(3t)…

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Q: Compute the matrix product in this exercise using paper and pencil. [5 6 7] =

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Q: 5. Give an example of a matrix A such that im(A) is in R2 is spanned by the vector A = %3D

A: Given that, A is a matrix such that imA is in ℝ2 is spanned by the vector 52

Q: Let A = a b c d and let k be a scalar. Find a formula that relates det(kA) to k and det(A). Find…

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Q: Give an example of a 2 x 2 matrix A such that im(A) =ker(A). %3D

A: Null space of a linear transformation: T:V(F)→V'(F) be a linear transformation then the null space…

Q: Find the two conditions on b1, b2, and bz which determine solvability of 4 8. 3 4 =6= b2 -6 -7 -8 b3

A: The objective is to form the equation involving b1, b2, and b3 that determine the solvability of the…

Q: 1. The given set with the given operations is not a vector space. Check all the properties and list…

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Q: 2. Suppose T : R³ → R³ is a linear map given by a matrix A, and that А 2 1 2

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Q: Find the kernel and nullity of the transformation T. Т(М) — М 0 1 1 2 1 2 M from R?x 2 to R2x2 T(M)…

A: The given question is solved below.

Q: For each problem find square matrices which satisfy the given conditions. You don't have to justify…

A: Since you have posted a question with multiple sub-parts, I will solve the first three subparts for…

Q: Given that B=([1 -2 2].[1 -1 3). ([0-3-2]) is a basis of R³ and C= ([1-3 0], [0 1 0]. [-3 11 1]) is…

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Q: 3. Find the general solution of the system of differential equations * - ()* d 8 -5 10 + 4°c (…

A: given ,system of differential equations…

Q: Problem 1. Consider the matrices [1 1 0] A = |0 2 2 0 0 3 1 3 2 A? = |0 4 10 0 0 9 1/3 1/2 -1/3 1/3…

A: Given matrices are, A=110022003, A2=1320410009, A-1=1-1213012-130013 Now, λ ia an eigen value of…

Q: Linear algebra

A: Consider the set

Q: Suppose for some unknown u, v, w, and a, a = 3ū+2v + w 22.1 Could the set {u, v, w} be linearly…

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Q: Let L be the line spanned by 2 Answer: 0 8 in R³. Find a basis of the orthogonal complement L¹ of L.…

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Q: Find a matrix with no zero entries that commutes with the given matrix A. 4 17 1 4

A: The detailed solution is as follows below:

Q: linear algebra

A: 6. The given matrix is

Q: Let B = {x²+x,-2x² + 3x + 3, 2x² – x – 2} be a basis of P2(R)

A: Given,            B=x2+x,  -2x2+3x+3,  2x2-x-2

Q: Use Cramer's Rule to solve for x2. xi + 2x2 +x3 = 2 3x1 – x2 - 2x3 = 7 X2 +x3 = -1

A: Here we have given one matrix and we have to find the value of x2 by using the Cremer’s rule.   Now…

Q: If not, why not? 1 6 4 -(0·0·0); 3 1 8 6 4. What is span ?

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Q: (3) (a) Let T be a surjective linear transformation from P7 W. Show that dim(W) dim(W). Lastly, the…

A: Given below the detailed solution

Q: Problem 2. Let V = span{e3, e-3z}, and let the linear transformation D : V → V be differentiation…

A: A linear transformation is a function from one vector space to another that respects the underlying…

Q: Linear algebra

A:

Q: Is the transformation below linear? Upload your proof below T(M) = M2 from R2x 2 to R2x 2 OLinear…

A: Not Linear

Q: List the eigenvalues of A. The transformation x→Ax is the composition of a rotation and a scaling.…

A: The given matrix, A=33-3333 We have to find the eigenvalues of A and rotation angle and the scale…

Q: Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C². 45 -54…

A: Given, The matrix A = 45-54   We have to find the eigen values and eigenspaces.

Q: Linear Methods

A: Given, x1x2˙=-37-563045x1x2+e4t26-19 i.e.  x1˙=-37x1-56x2+26e4tx2˙=30x1+45x2-19e4t Given the…