Write the linear system in matrix form: dx/dt = -3x + 4y + e* sin(2t) dy/dt = 5x + 9z + 4et cos(2t) dz/dt = y + 6z - et %3D 2) Write the given system without the use of matrices: 3 sin t + dt 2t +

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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.

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

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

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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

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

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Q: The linear transformation T(f) = f+ f'' from C 0 C is an isomorphism. True False

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

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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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A: The given question is solved below.

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Q: Linear Algebra

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

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A: We have to identify redundant vectors.

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

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

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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…

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

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.