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Solve the system by using the inverse of the coefficient matrix. -5x1 + 4x2 = -9 -15x1 + 12x2 = -2 (-9, -2) (3, 3) (9/5, 5/4) No solution Let T be the linear transformation whose standard matrix is A = Determine whether the linear transformation T is one-to-one and whether it maps R3 onto R3. T is one-to-one, but does not map R3 onto R3. T is one-to-one and maps R3 onto R3. T is not one-to-one, but maps R3 onto R3. T is not one-to-one and does not map R3 onto R3. Describe geometrically the effect of the transformation T. Let A = . Define a transformation T by T(x) = Ax. Horizontal shear Vertical shear Projection onto x2-axis O Projection onto x1-axis Perform the matrix operation. Let A = and B = Find 4A + B. Let A = and b = [1 24 25]. Define a transformation T: R3 rightarrow R3 by T(x) = Ax. If possible, find a vector x whose image under T is b. Otherwise, state that b is not in the range of the transformation T. [-5 2 -2] [-5 -2 2] [-5 -2 0] b is not in the range of the transformation T. .The columns of I3 = are e1 = [1 0 0], e2 = [0 1 0], e3 = [0 0 1]. Suppose that T is a linear transformation from R3 into R2 such that T(e1) = [2 -4], T(e2) = [-5 0], and T(e3) = [-6 1], Find a formula for the image of an arbitrary x = [X1 X2 X3] in R3.
Explanation / Answer
1)c
2)b
3)b
4) d
5)d
6)b
