a) Option C is correct.
b) Option A is correct.
c) Option C is correct.
d) Option B is correct.
e) Option A is correct.
f) Option A is correct.
a. Every matrix equation Ax b corresponds to a vector equation with the same solution set....
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
Mark each statement True or False. Justify each answer. a. A homogeneous system of equations can be inconsistent. Choose the correct answer below. O A. True. A homogeneous equation can be written in the form Ax o, where A is an mxn matrix and 0 is the zero vector in R". Such a system Ax -0 always has at least one solution, namely x-0. Thus, a homogeneous system of O B. True. A homogeneous equation cannot be written in the...
a) Write the augmented matrix for the linear system that corresponds to the matrix equation AX = b b) solve the above system c) write the solution as a vector A= 0 4 5 -1 3 2 and b= 1 24 5 4 2
Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x1 +4x2+8X3 = 16 - 12X1 - 12X2 - 24x3 = - 48 - 6x2 - 6x3 = 18 4x7 +4x2+8X3 = 0 - 12X1 - 12X2 - 24x3 = 0 - 6x2 - 6x3 = 0 X1 Describe the solution set, x = X2 of the first system of equations...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
linear algebra question easy, please answer fast with steps Mark each statement True or False. Justify each answer. Here A is an mxn matrix. Complete parts (a) through (e) below a. If B is a basis for a subspace H, then each vector in H can be wrben in only one way as a linear combination of the vectors in B. Choose the correct answer below O A. The statement is false. Bases for a subspace H may be linear...
Write each statement as True or False (a) If an (nx n) matrix A is not invertible then the linear system Ax-O hns infinitely many b) If the number of equations in a linear system exceeds the number of unknowns then the system 10p solutions must be inconsistent ) If each equation in a consistent system is multiplied through by a constant c then all solutions to the new system can be obtained by multiplying the solutions to the original...
(a) Suppose we want to solve the linear vector-matrix equation Ax b for the vector x. Show that the Gauss elimination algorithm may be written bAbm,B where m 1, This process produces a matrix equation of the form Ux = g , in which matrix U is an upper-triangular matrix. Show that the solution vector x may be obtained by a back-substitution algorithm, in the form Jekel (b) Iterative methods for solving Ax-b work by splitting matrix A into two...
3. If 3V1-2V2 + V3 w, and A is the matrix whose columns are V1, V2 and V3 and x is an unknown vector, determine whether each statement is ALWAYS SOMETIMES or NEVER true A. The equation Ax w is consistent. B. The equation Ax w is inconsistent. C. The equation Aw = x is consistent. D. The equation Aw =x is inconsistent.
Mark each statement as True or False and justify your answer. a) The columns of a matrix A are linearly independent, if the equation Ax = 0 has the trivial solution. b) If vi, i = 1, ...,5, are in RS and V3 = 0, then {V1, V2, V3, V4, Vs} is linearly dependent. c) If vi, i = 1, 2, 3, are in R3, and if v3 is not a linear combination of vi and v2, then {V1, V2,...