Q-3: [x 4 -6 -7 [1 3 Let A = -3 x+1 10 and B3 0 0 -3 0 LO -1 a) Find values of x for which the matrix A is singular. b) Find a matrix X such that (A-1)TX = B if x = −1. c) Is the linear system has unique solution at x = -5. Justify.

Solve: {4x3z=53y+2z=73x+4y=6 .

Write the system of equations that corresponds to the augmented matrix: [111423181113] .

Use Cramers rule to solve 2x-y+2z=6x-y+z=2x+y+2z=9.

Explain the difference between the row-echelon form and the reduced row-echelon form of a matrix.

Show that the system of linear equations 2x1+3x2+x3=5x14x2+5x3=8 can be written as the matrix equation [231145][x1x2x3]=[58].

Determine if the statement is true or false. If the statement is false, then correct it and make it true. For the product of two matrices to be defined, the number of rows of the first matrix must equal the number of columns of the second matrix.