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Matrices: Vectors and Planes

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1) Let v_1 = 1 v_2 = -3 and y = h.
[ 0 ] [ 8 ] [-5]
[-2 ] [ 8 ] [-3]
For what value of h is y in the plane generated by v_1 and v_2?

2) Compute the product why (a) the definitions and (b) the raw vector rule.

8 3 -4 * 1
5 1 2 * 1
* 1

3) Write the given linear system first as a vector equation and then as a matrix.

8x_1 - x_2 = 4
5x_1 + 4x_2 = 1
x_1 - 3x_2 = 2

4) Given A and B, write the augmented matrix for the linear system that corresponds to the matrix eg. Ax = b. Then solve the system and write the solution as a vector

A = 1 2 1
-3 -1 2
0 5 3

b = 0

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Solution Summary

Matrix problems involving vectors and planes, products and Ax = b are investigated in this solution. The solution is provided in an attached Word document.

Solution Preview

1. From the condition, we know that y = av1 + bv2 for some real numbers a, b. So we get a system of equations.

(see attached)

From the last two equations, we can ...

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