Q.3 The matrix A = 3 0 1 yields a shearing transformation, which leaves the y-axis unchanged. Sketch its effect on x-axis, by indicating what happens to (1,0), (2,0) and (-1,0) and how the whole axis is transformed. [12] Q.4 Let 7: 3 - IR3 be a mapping defined by T(X1, X2, X3) = (X1 + X2 - 2x3, -X1 + 2x2 -X3, 4x2 - 5x3). Show that T' is linear. [12] Q.5 Write the vector form of the general solution of the given system of linear equations. Determine whether the system is linearly independent or dependent. [14] -X1 - 2x3 - X4 - 5x5 = 0 -X2 + 3x3 + 2x4 = 0 -2x, + x2 + X3 - X4 + 8X5 = 0 3x1 - X2 - 3x3 - X4 - 15x5 = 0