Hi, i have two question to ask you guy about

The first,

Evaluate det(A) and use your answer to give the values of t which is a real number for which A is non singular

[(3-t) 0 7 5]

[(t-3) t 1 1] = A, (4x4 matric)

[0 -t 4t 2]

[0 0 2t+4 t+5]

I'm not sure about how to handle this question. Is it possible to handle this question be reduce this matrix to row-echelon form? so that I can find the determinant afterward.

The second question, I'm not sure if what I did is right or not for the first part, and for the second part I have no idea how to do it.

Consider the following three points in R^3

P=(1,-1,2) Q=(1,2,-3) R=(-1,4,1)

a) calculate QP (hat), QR (hat) and QP(hat) x QR(hat)

QP(hat) =(1, -1, 2) - (1,2,-3) = (0,-3,5)

QR(hat) =(-1,4,1) - (1,2,-3)= (-2,2,4)

QP(hat) x QR(hat) = (0,-3,5) x (-2,2,4) = 0x-2 + (-3x2) + (5x4)=20-6= 14 (is it)?

b) Use the cross product to find the area of the triangle with vertices P,Q and R

What cross-product I supposed to use? and how do I use it...

Best Regards

Junks