[CUSTOM SOLUTION] Matrix And Linear Algebra

Question 1.Find x and y so that [2x ???? y; x + 3y] = [1; 25]:Question 2.Write the vector [3; 5] as a linear combination of [6; 4] and [3; 1]:Question 3.Find the angle between the vectors [1; 2; 2] and [3; 4; 5]:Question 4.(a) Find the cross product [2; 3; 4] [7; 6; 5]:(b) Find a unit vector that is orthogonal to both [2; 3; 4] and [7; 6; 5]:(c) Compute the dot product of the unit vector that you found in Part (b) with each of [2; 3; 4] and [7; 6; 5]:Question 5.Find the shortest vector among the following 3 vectors:[3; 0; ????5]; [????1; 2; ????4]; [2; 3; 2]Question 6.Find the equation of the line that passes through the points 1; 3; 4) and (5; 8; 6):Question 7.Find the equation of the plane that passes through the point (1; 3; 4) and is normal to [4; 3; 2]:

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