# Linear Algebra Questions and Answers

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Linear AlgebraName Date 3 24 23 Class 802 ALL WORK IS SHOWN ON LOOSE LEAF DIRECTIONS PLEASE READ THE FOLLOWING SCENARIO TO ANSWER THE PROMPTS THAT FOLLOW I Ms Karla was driving to Las Vegas in her electric vehicle Her vehicle gets 250 miles for every 4 5 of battery life a What is the rate of change b Grapn the function Sur com use your equation rate of change to answer q6 If ms karla drives 600 miles how much life will she have used battery 0 miles can ms karla drive on

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Linear Algebra2122 Need Help Read It 2 Points DETAILS SALGTRIG4 8 3 056 Find the product z1z2 and the quotient Express your answers in polar form Z cos 45 sin 45 22 cos 120 sin 120

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Linear AlgebraFind the work done by the force field F 2 2 x in moving a par ticle along the curve C where C is the intersection curve of the plane x z 1 and the ellipsoid x 2y z 1 oriented counterclockwise when viewed from positive z axis

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Linear AlgebraUse the simplex method to solve the linear programming problem Maximize z 4x 7x subject to X 4x2 555 3x 2x 33 x 20 X 20 with Set up the initial simplex tableau Select the correct choice below and fill in the answer boxes to complete yo choice OA X OB X2 S 1 X N Hi 2 X2 1 2 S3 1 N Z 1 55 33

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Linear AlgebraUltrasound is used in medicine both for diagnostic imaging Fig P17 9 page 526 and for therapy For diagnosis short pulses of ultrasound are passed through the patient s body An echo reflected from a structure of interest is recorded and the distance to the structure can be determined from the time delay for the echo s return To reveal detail the wavelength of the reflected ultrasound must be small compared to the size of the object reflecting the wave The speed of ultrasound in human tissue is about 1 500 m s nearly the same as the speed of sound in water a What is the wavelength of ultrasound with a frequency of 2 40 MHz b In the whole set of imaging techniques frequencies in the range 1 00 MHz to 20 0 MHz are used What is the range of wavelengths corresponding to this range of frequencies B Benoit Photo Researchers Inc Figure P1794 view of a fatur

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Linear Algebra50 1 0 0 1 0 1 0 1 0 0 0 0 0 0 10 1 0 0 1 1 0 Exercise 10 0 9 B level Consider the transpose matrix to the one above 50 and call it do Show that this matrix represents the linear map do R X R X which is induced by sending basis element 1 ej to the vector 1 p 1 Pi Exercise 10 0 10 C level Compute the determinant of 60 above What does this tell us about the kernel of 50 B12 B02 B01 to12 The matrix which is Similarly I can define a linear map 6 R x R X by Bij eij associated to this linear map is 6 1 1 1 0 0

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Linear Algebraa relationship is impossible So by the above lemma we have an injective linear map Exercise 10 0 5 C level Let X A Give 5 elements in R X Can you write something down using scalars el from X and other familiar symbols but that is not in R X

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Linear AlgebraLet P2 be the vector space of all real polynomials of degree at most 2 Let P P2 P3 E P2 be given by pi z 2 p2 x 2x x and p3 x x ar a 4 marks Find the condition on a ER that ensures that P1 P2 P3 is a basis for P2 You are free to assume that the polynomials 1 2 and are linearly independent b 2 marks In the case that a 4 write the polynomial p x 4 write the polynomial p x combination of p1 p2 and p3 Can you write the polynomial p x 2 r r as a linear combination of p p2 and P3 when a Justify your answer 2 1 as a linear

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Linear AlgebraExpress the vector v with initial point P and terminal point Q in component form P 7 8 Q 9 7 11

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Linear AlgebraQuestion 3 Jaden throws a ball straight up in the air with an initial speed of 40 ft sec from a height of 7 ft Fill in the parametric equation that describes the vertical motion of the ball as a function of time t y t 16t2 Select Select Select 2 pt Select

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Linear AlgebraThe figure shows a medicine wheel which is a Native The central angle in Type an integer or a simplified traction The central angle in degrees is approximately inal spokes in the wheel al equally spacedure The figure shows a medicine wheel which is a Native American structure This circular structurebis perhaps 2500 yr old There are 27 aboriginal spokes in the wheel all equally spaced a Find the measure of each central angle in degrees and in radians The central angle in degrees is approximately Type an integer or a simplified fraction The central angle in radians is approximately Simplify your answer O Type an exact answer in terms of n Use integers or

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Linear Algebra26 IV fluids 1000 mL blood transfusion 2 units 360 mL per unit 6 oz water

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Linear Algebra6 3 Points DETAILS SMITHNM13 13 1 For the spinner below assume that the pointer can r B