6. Show that the two planes: 5x – 4y – 5z = –8, and - 2x + 3y + 9z 13 | intersect in a line, and find a vector equation for this line. Hint: view this problem as a linear system, and express the solution vector as the sum of a constant vector and a vector multiplied by z. Verify that the constant vector satisfies both equations, which makes it a particular solution that represents a point on both planes.

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Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the equation r1(t)=r2(t) may not produce all the points where the graphs of these functions intersect.  Please Provide Unique Answer. Thank you!

5. Show that the vectors a = 3i-j+ 4k, b =i-3j-2k and e = 4i– 3j+2k are linearly independent. Find numbers a, B and y such that d = 2i + 3j – k can be expressed in the form d= aa + Bb + 7c.

Suppose the vector x characterizing the antigenic state of an influenza virus population changes from one season to the next according to the equation 23 Xt + 1 ¹ -[3.39]** 0 0.9 If the vector in the current season is [...] what was the vector in the previous influenza season? ↓ 1

Express the vector v =-1 as a linear combination of the vectors --3 V1 0,v2 4 and v3 -4 , if possible. Show all of the steps that you used %3D 3 -2 11 in obtaining your solution. 3.