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![Solve the matrix equation for y.
1 2
31-21²
2 6 3
2
0-1/10
O There is no correct answer.
0-1
* Previous
[1 3 7
] -³ [1] + [8
-6 -19
3
30
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![For what value(s) of h are the following vectors linearly independent?
3
H
15
Oh=2
0 h 2
0h=-2
Oh=2 or h=-2
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J
and v
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h
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-10
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- For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.a. Is it possible to find an elementary matrix E1 such that E1A = B? If yes, what is E1? If no, justify. b. Is it possible to find an elementary matrix E2 such that E2B = C? If yes, what is E2? If no, justify. Please show all of the work given is in the image.1. Solve A-1 using Co-Factor Method 2. From #1, Calculate the AA-1=1. What is I? Is it a Matrix? What are its elements?
- (4) Given matrix A = ( 2 −1 3 5 ) , and that h(T) = T 2 − 2T − 7, find h(T). ??????? ??? ? (1) A course repeater claims that his brother who did some Calculus at college years ago, but currently on some cough medication, believes that the first derivative of f(x) = (2x 2 − 1)(x 2 + 3) x 2 + 1 is f ′ (x) = [ 4x 2x 2 − 1 + 2x x 2 + 3 − 2x x 2 + 1 ][ (2x 2 − 1)(x 2 + 3) x 2 + 1 ] and that the first derivative of g(x) = (x 2 + 8) 7 (2 − 3x2) 5 is g ′ (x) = [ 14x x 2 + 8 + 30x 2 − 3x2 ] [ (x 2 + 8) 7 (2 − 3x2) 5 ] Using the product, qoutient and chain rules you learnt in Unit 7 of this Course, could you confirm whether his brother is right, wrong or a little tipsy. (2) In the following triangle below, the degree measures of the three interior angles and two of the exterior angles are represented with variables and expressions. (a) Find the size of each of the interior angle.Solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of Albert Einstein, "Everything should be made as simple as possible, but not simpler.") Assume that all matrices are invertible. XA2 = A-1Solve the given matrix equation for X. Simplify your answers as much as possible. (In the words of Albert Einstein, "Everything should be made as simple as possible, but not simpler.") Assume that all matrices are invertible. AXB = (BA)2
- We are given the matrix (1 -a) (c a) What is the value of a if one of the eigenvalues of the matrix is 2(c+1) with a corresponding eigenvector (-2,1)Solve the given matrix equation for X. Simplify your answers as much aspossible. (In the words of Albert Einstein, \"Everything should be made as simple as possible, but not simpler\") Assume that all matrices are invertible. XA2 = A-1You are given the matrix: [-7 4][4 -13] and told that the eigenvector corresponding to the eigenvalue -15 can be written in the following form: [1 y]T What is the expression for the value of y?
- Write down the 3 by 3 matrix that has aij = 2i - 3j. This matrix has a32 = 0, but elimination still needs E32 to produce a zero in the 3, 2 position. Which previous step destroys the original zero and what is E32 ?solve using matrix exponentials: For A=[(-1,0),(-2,1)] calculate I+tA+t^2/2 A^2 + t^3/6 A^3: [(_,0),(t(-t^2-6) / 3,_)] The actual value of e^(0.1A), to six decimal places, is [(0.904837, 0),(-0.200334, 1.105170)]. What do you get when you plug t = 0.1 into the approximation e^(tA)~~I+tA+t^2/2 A^2 + t^3/6 A^3? (Give six decimal places with no rounding.)If the trace of 2x2 matrix A is -7 and det(A)=10 then the eigenvalues of A are A. 5 and 2 B. 3 and 4 C. 10 and 1 D. -10 E. none of them