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Trigonometry

The foot, F, of a hill and the base B, of a vertical tower TB, 27 metres tall, are on the same horizontal plane. From the top, T, of the tower, the angle of depression of F is 32.7 degrees. P is a point on the hill 27.5 metres away from F along the line of greatest slope. T, B, F and P all lie in the same vertical plane. The angle of depression of P from T is 22.6 degrees. a) Draw a sketch to represent the information given above b) Show that: (i) TF is 50m approximately (ii) sin TPF = 7/22 approximately c) Calculate: (i)the gradient of the hill (ii) the height, in metres, of P above F , giving your answer correct to the nearest metre. Note: ... click for more

Subject:

Math

Topic:

Other

Posting ID:

2617

OTA ID:

103020

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Matrix Theory

See attached file for full problem description with symbols and equations. --- Definition 11.1 An orthogonal projection operator is a linear transformation such that and . Question: If W is a subspace of V, prove that P_w is an orthogonal projection. (P_w is P sub w)

Subject:

Math

Topic:

Other

Posting ID:

2649

OTA ID:

101298

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Matrix Theory

Show that Null (A) and Im(A) are not orthogonal. (see Matrix in attached file)

Subject:

Math

Topic:

Other

Posting ID:

2650

OTA ID:

101298

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Matrix Theory

Prove that A is normal if and only if A-A^* and A+A^* commute.

Subject:

Math

Topic:

Other

Posting ID:

2651

OTA ID:

101298

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Matrix Theory

Show that each matrix type is normal. 1. Hermitian 2. skew-Hermitian 3. unitary 4. symmetric 5. skew-symmetric 6. orthogonal

Subject:

Math

Topic:

Other

Posting ID:

2652

OTA ID:

101262

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