 # Vector and Linear Algebra

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"Vector geometry"
1. Decompose vector C = (0,9) in the vectors a = (5,4) and b = (1, -1).
2. Given. Find.
3. Calculate the projection of the vector on the axis of the vector when.
4. Calculate the cosine of the angle between the vectors.
5. Find the moment of force applied at a point with respect to the point, and the unit and the direction cosines of the force vector.
6. Find the area of \u200b\u200bthe parallelogram constructed on the vectors.
7. At what vectors are coplanar?
8. Find the equation of the line passing through the point parallel to the line connecting points.
9. In the square AVSD given vertex and the intersection point of the diagonals. Be sides of the equation and find the coordinates of the remaining vertices.
10. Write the equation of the plane that passes through the origin and has a normal vector.
11. Create a canonical and parametric equation of the line passing through the point parallel to the line:.
Write the equation of the plane passing through the line.

Linear algebra
1. Calculate the determinant of the third order, using the definition. Result check the expansion of the determinant of any row and any column:
2. Solve the system of linear equations by Cramer's rule and using the inverse matrix:
3. Determine whether the vectors
linearly dependent.
4. Investigate the system of linear equations on the compatibility and consistency of the case to find a solution by Gauss:
5.Nayti transformation matrix expressing z1, z2, z3, by x1, x2, x3, where:
6. Find the eigenvectors and eigenvalues \u200b\u200bof the linear transformation given by the matrix.

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