Question # 2: Consider an open economy with three industries: coal-mining operation, electricity-generating plant and an auto-manufacturing plant. To produce $1 of coal, the mining operation must purchase $0.1 of its own production, $0.30 of electricity and $0.1 worth of automobile for its transportation. To produce $1 of electricity, it takes $0.25 of coal, $0.4 of electricity and $0.15 of automobile. Finally, to produce $1 worth of automobile, the auto-manufacturing plant must purchase $0.2 of coal, s0.5 of electricity and consume $0.1 of automobile. Assume also that during a period of one week, the economy has an exterior demand of $50,000 worth of coal, $75,000 worth of electricity, and $125,000 worth of autos. Lets suppose that equation for production (output) is given by P = (1 - A)d. Where A is the coefficient matrix having each sector's purchase as column entries and d is the demand vector. I is corresponding n*n square matrix Find the production level of each of the three industries in that period of one week in order to exactly satisfy both the internal and the external demands.

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

A:

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 -

A:

Q: Find a basis of the image of the matrix below. 1 1 1 A = 125 1 3 7

A: Given matrix is A=111125137 We have to find the basis of the image of A. First of all reduce the…

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

A:

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…

A:

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: Linear algebra

A:

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…

A:

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

A:

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…

A:

Q: Linear Algebra

A: We are given that W = span{x, y}.  Here, we need to construct an orthonormal basis for W. In other…

Q: Consider the vectors V1, V2, V3 and b. 1 2 8 -2 V1 ,V3 -13 6. 12 18 Write b as a linear combination…

A:

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…

A:

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

A:

Q: Define the linear transformations T:R R2 and S: R R so that 3. X1 + X2 -X2 and S X2 -I - 12 a.) Is…

A:

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: 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 ?

A:

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: 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…