Linear algebra and matrix

Ex: x + y − z = −5x − y − 7z = 70.75x − 0.5y + 0.25z = 18x + y + z = 1   If a=x, b=y, and c=z, what is d?     

Let S={X1,X2,X3} be a linearly independent set of vectors in R^3. How to determine whether T={2X1 + X2 - 2X3,4X1+ 3X2,3X1 + 2X2 - X3} is linearly independent. Justify your answer please.

If X1,X2 and X3 are vectors in R3 such that {X1,X2} and {X1,X3} are linearly independent sets, then {X1,X2,X3} is a linearly independent set.

               2 1 0                   1 0 1Let A = [ 1 0 1 ] and B = [ 2 0 1 ]                0 3 0                  0 1 1 Find the matrix X such that (2X + A)-1 = B.

If A is a 2 x 2 matrix such that AAT (Transpose) = 0, then A = 0.

what matrix is formed when a matrix is pre-multiplied by its inverse matrix  I have no idea about this question it confuses me

Given    T(  |1|)  = |5|      |0|      |9|     T( |0|  = |5|     |1|     |-7|     Find a matrix such that   T(v)=      |         |    (v)               |          |    

so my question is    Determine the value of h such that the matrix is the augmented matrix of a linear system with infinitely many solutions.   /6    -5   /    8     / /18    h  /    24 ... more

2 x + 9 y + 3 z = -8.   /x/            /      /          /     /            /      / /y/    =      /     /    +    /     /s  +       /      /t /z/            /     /          /     /           ... more

4x+5y=a 5x+6y=b   so   x=? y=?

Determine the value of k for which the system   x+y+2z=0 x+2y-3z=-2 3x+9y+kz=-11   has no solutions.   so, what's k = ?

  -6    1    7-6    1    4-12  2    11   this is a matrix  what is the rank of the above matrix?

  {        -5  -3  -6     }                   [   -4    ]           [     x     ]{        -5   1   8      }        *        [    6      ]   =    [     y     ] {        -8   7  -6      }         ... more