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1. ### Consider the following three points in R^3

Consider the following three points in R^3: P(−2, 5, 1), Q(0, 3, 1), R(3, 3, 5) and let a =P Q(vector), b =P R (vector), c =QR (vector) (a) Calculate the following if possible, or explain why it is not possible to do so: (i) a × b (ii) c × (a · b) (vi) (b × a) · c (vi) (a · b) · c (b) Use the...
2. ### Use elementary row operations to find the reduced row echelon form

(a) Use elementary row operations to find the reduced row echelon form of the matrix M = [1 0 4 0 0 5 0 1 −2] (b) For the elememtary row operations you used in (a), construct the corresponding elementary matrices. Clearly identify which matrix corresponds to which row operation. (c) (i)...
3. ### A consistent system of linear equations in 14 unknowns is reduced to row echelon.....

A consistent system of linear equations in 14 unknowns is reduced to row echelon form. There are then 10 non-zero rows (i.e. 10 pivots). How many parameters (free variables) will occur in the solution?
4. ### Determine values of k for which linear system of eqns has...

A linear system with three variables has augmented matrix that is row-equivalent to the following matrix:   k + 3 2 k − 4 =3 0 2 −9 =5 0 0 k^2 + k − 2= k − 1   Determine the values of k for which the system has: (a) exactly one solution, (b) infinitely...
5. ### Write augmented matrix, apply Gauss-Jordan, and solve system

help needed immediatly before tommorrow: (a) Write down the augmented matrix corresponding to the linear system: 4x1 + 2x2 − 7x3 − 11x4 = 5 2x1 + 1x2 − 2x3 − 4x4 = 2 4x1 + 2x2 − 10x3 − 14x4 = 6 (b) Use Gauss-Jordan elimination to reduce this matrix to reduced row-echelon form. (c) Solve the...