8.4 Matrix Algebra

8.4 Matrix Algebra

Adding and subtracting matrices, multiplying matrices by scalars, multiplying matrices, finding inverses of matrices, and using inverse matrices to solve systems of linear equations

Diagonalizing 3×3 Matrix – Full Process [Passing Linear Algebra]

Diagonalizing 3×3 Matrix – Full Process [Passing Linear Algebra]

Important high level asides: 1) 3:07 (remember, 1 ≤ geo mult ≤ alg mult, so since λ=1 has alg mult of 1, it’s geo mult is automatically 1) 2) 6:15 (the point where we find out A is diagonalizable) Finding Eigenvalues: 0:40 Finding Basis for Eigenspaces: 4:20 Putting it all together: 10:06

Lecture 4: Linear algebra (cont), matrix calculus, MATLAB

Lecture 4: Linear algebra (cont), matrix calculus, MATLAB

Lecture 4: Linear algebra (cont), matrix calculus, MATLAB This is a lecture video for the Carnegie Mellon course: ‘Computational Methods for the Smart Grid’, Fall 2013. Information about the course is available at http://www.cs.cmu.edu/~zkolter/course/15-884/

Puzzle Problem – Bridge Crossing at Night

Puzzle Problem – Bridge Crossing at Night

Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! 🙂 https://www.patreon.com/patrickjmt !! Puzzle Problem – Bridge Crossing at Night

Lesson 32 – The set is a basis for Let is a linear transformation such that and

Lesson 32 – The set is a basis for Let is a linear transformation such that and

Leave a tip for good service: https://paypal.me/jjthetutor Let b_1=(1,1) and b_2=(1, 0). The set is a basis for. Let is a linear transformation such that. Then the matrix of relative to the basis is and the matrix of relative to the standard basis for Student Solution Manuals: https://amzn.to/2WZrFnD More help via http://jjthetutor.com Download my eBooks…

11.88 … DATA You are a construction engineer working on the interior design of a retail store in a mall. A 2.00-m-long uniform bar of mass 8.50 kg is to be attached at one end to a wall by means of a hinge that allows the bar to rotate freely with very little friction. The bar will be held in a horizontal position by a light cable from a point on the bar (a distance x from the hinge) to a point on the wall above the hinge. The cable makes an angle u with the bar. The architect has proposed four possible ways to connect the cable and asked you to assess them: (a) There is concern about the strength of the cable that will be required. Which set of x and u values in the table produces the smallest tension in the cable? The greatest? (b) There is concern about the breaking strength of the sheetrock wall where the hinge will be attached. Which set of x and u values produces the smallest horizontal component of the force the bar exerts on the hinge? The largest? (c) There is also concern about the required strength of the hinge and the strength of its attachment to the wall. Which set of x and u values produces the smallest magnitude of the vertical component of the force the bar exerts on the hinge? The largest? (Hint: Does the direction of the vertical component of the force the hinge exerts on the bar depend on where along the bar the cable is attached?) (d) Is one of the alternatives given in the table preferable? Should any of the alternatives be avoided? Discuss.

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.

11.87 .. DATA You need to measure the mass M of a 4.00-mlong bar. The bar has a square cross section but has some holes drilled along its length so you suspect that its center of gravity isn’t in the middle of the bar. The bar is too long for you to weigh on your scale. So first you balance the bar on a knife-edge pivot and determine that the bar’s center of gravity is 1.88 m from its left-hand end. You then place the bar on the pivot so that the point of support is 1.50 m from the left-hand end of the bar. Next you suspend a 2.00-kg mass 1m12 from the bar at a point 0.200 m from the left-hand end. Finally you suspend a mass m2 = 1.00 kg from the bar at a distance x from the left-hand end and adjust x so that the bar is balanced. You repeat this step for other values of m2 and record each corresponding value of x. The table gives your results. (a) Draw a free-body diagram for the bar when m1 and m2 are suspended from it. (b) Apply the static equilibrium equation gtz = 0 with the axis at the location of the knife-edge pivot. Solve the equation for x as a function of m2. (c) Plot x versus 1>m2. Use the slope of the best-fit straight line and the equation you derived in part (b) to calculate that bar’s mass M. Use g = 9.80 m>s2. (d) What is the y-intercept of the straight line that fits the data? Explain why it has this value.

University Physics with Modern Physics lessons by JJtheTutor. Designed to teach students problem solving skills, test taking skills and how to understand the concepts.