12. (a) Find all values of c that would make the following matrix invertible. Re

Question

12. (a) Find all values of c that would make the following matrix invertible. Recall that an n x n

matrix is invertible if and only if its rank is n:

inverse.

(c) Give an example of a 2 x 2 matrix that is not invertible.

13. (a) Find a parametric equation of the plane through the point (2; 5; 8) that is parallel to the

(b) Find a parametric equation of the plane with cartesian equation 2x + 7y + z = 12.

(c) Find a parametric equation of the line through the point (2; 3;??4) that is parallel to the

12. (a) Find all values of c that would make the following matrix invertible. Recall that an n x n matrix is invertible if and only if its rank is n: begin{bmatrix} 1 & 1&1 1& 9& 0 1&c; & 3 end{bmatrix} (b) Consider the 2 2 matrix A = begin{bmatrix} 1 & -3 6&9 end{bmatrix} . Determine if A is invertible. If so give its inverse. (c) Give an example of a 2 x 2 matrix that is not invertible. 13. (a) Find a parametric equation of the plane through the point (2; 5; 8) that is parallel to the vectors begin{bmatrix} 7 -9 1 end{bmatrix} and begin{bmatrix} 1 0 8 end{bmatrix} . (b) Find a parametric equation of the plane with cartesian equation 2x + 7y + z = 12. (c) Find a parametric equation of the line through the point (2; 3;??4) that is parallel to the vector begin{bmatrix} -9 3 1 end{bmatrix} . (d) Find a parametric equation of the line through the point (1;??5) that is parallel to the vector begin{bmatrix} -2 1 end{bmatrix} .

Explanation / Answer

12. (a)

27-3+c-9 = 0, c = -15

hence except for c = -15, for al others value, matrix is invertible

(b)

(c) a matrix with all the elements same is not invertible

? A1 A2 1 1/3 1/9 2 -2/9 1/27

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