Determine which matrices are in reduced echelon form and which others are only in echelon form. Is matrix a in reduced echelon form, echelon form only, or neither? (a) Echelon form only (b) Reduced echelon form (c) Neither Is matrix b in reduced echelon form, echelon form only, or neither? (a) Reduced echelon form (b) Echelon form only (c) Neither Is matrix c in reduced echelon form, echelon form only, or neither? (a) Reduced echelon form (b) Echelon form only (c) Neither
Row reduce the matrix to reduced echelon form. Identify the pivot positions in the final matrix and in the original matrix, and list the pivot column. Row reduce the matrix to reduced echelon form and identify the pivot positions in the final matrix: The pivot positions are indicated by bold values. Choose the correct answer below. Identify the pivot positions in the original matrix The pivot positions are indicated by bold values. Choose the correct answer below. List the pivot columns. Select all that apply. Column 3 Column 4 Column 2 Column 1
Find the general solution of the system, whose augmented matrix is given below. Select the correct choice below and, if necessary, fill the answer box(es) to complete your choice.
Find the general solution of the system, whose augmented matrix is given below. Select the correct choice below and, if necessary, fill the answer box(es) to complete your choice.
Find the general solution of the system, whose augmented matrix is given below. Select the correct choice below and, if necessary, fill the answer box(es) to complete your choice.
Choose h and k such that the system has (a) No solution (b) a unique solution and (c) many solutions. x1 + hx2 = 5 2x1 + 4x2 = k
In some cases, a matrix may be row reduced to more than one matrix in reduced echelon form, using different sequences of row operations. Determine whether the statement below is true or false. Justify the answer. Choose the correct answer below. A. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might B. The statement is true. It is possible for there to be several different sequences of row operations that row reduce a matrix C. The statement is false. Each matrix is row equivalent to one and only one reduced echelon matrix. D. The statement is false. For each matrix, there is only one sequence of row operations that row reduces it.
Determine whether the statement below is true or false. Justify the answer. The echelon form of a matrix is unique. Choose the correct answer below. A. The statement is true. The echelon form of a matrix is always unique, but the reduced echelon form of a matrix might B. The statement is false. Neither the echelon form nor the reduced echelon form of a matrix are unique. They depend on the row operations performed C. The statement is false. The echelon form of a matrix is not unique, but the reduced echelon form is unique. D. The statement is true. Both the echelon form and the reduced echelon form of a matrix are unique. They are the same.
Use the accompanying figure to write each vector listed as a linear combination of u and v. Vectors c, x, y, and z Write c as a linear combination of u and v. (Type integers or decimals.) Write x as a linear combination of u and v. (Type integers or decimals.) Write y as a linear combination of u and v. (Type integers or decimals.) Write z as a linear combination of u and v.
Write a vector equation that is equivalent to the given system of equations. x2 + 2x3 = 0 4x1 + 9x2 - x3 = 0 -x1 + 6x2 - 8x3 = 0
List 5 vectors in span{v1, v2}. Do not make a sketch. v1 = [6 2 -5)], v2 = [-5 3 0] List five vectors in Span{v1, v2} (Use the matrix template in the math palette. Use a comma to separate vectors as needed. Type an integer or a simplified fraction for each vector element. Type each answer only once.)
Let a1 = [1 5 -1], a2 = [-5 -18 3], b = [5 4 h]. For what value(s) of h, is b in the plane spanned by a1 and a2?
Give a geometric description of span {v1, v2} for the vectors v1 = [20 25 -5)] and v2 = [12 15 -3] choose the correct answer below. A. Span {v1, v2} is R^3. B. span {v1, v2} cannot be determined with the given information. C. span {v1, v2} is the set of points on the line through v1 and 0. D. span {v1, v2} is the plane in R^3 that contains v1, v2 and 0.
Construct a 3×3 matrix A, with nonzero entries, and a vector b in R^3 such that b is not in the set spanned by the columns of A. Choose the correct answer below.
An example of a linear combination of vectors v1 and v2 is the vector 1/2 v1 Determine whether the statement below is true or false. Justify the answer. Choose the correct answer below. A. The statement is true because 1/2v1 = 1/4 v1 + 1/4 v2 B. The statement is true because 1/2 v1 = 1.v1 + 0.v2 C. The statement is false because v1 cannot be expressed as a multiple of v2. D. The statement is false because a linear combination of v1 and v2 needs to involve both of those vectors.
Determine whether the statement below is true or false. Justify the answer. The weights c1, . . . , cp in a linear combination c1v1 + • • • + cpvp cannot all be zero. Choose the correct answer below. A. The statement is false. Setting all the weights equal to zero results in the vector 0. B. The statement is true. Setting all the weights equal to zero results in the vector 0. C. The statement is false. Setting all the weights equal to zero does not result in the vector 0. D. The statement is true. Setting all the weights equal to zero does not result in the vector 0.
The set Span {u, v} is always visualized as a plane through the origin. Determine whether the statement below is true or false. Justify the answer. Choose the correct answer below. A. The statement is false. Although the set Span {u,v} is always visualized as a plane, it is not always through the origin. B. The statement is true. The set Span {u,v} is always visualized as a line in R^3 that contains u, v, and 0 C. The statement is true. The set Span {u,v} is always visualized as a plane in R^3 that contains u, v, and 0. D. The statement is false. It is often true, but Span {u,v} is not a plane when v is a multiple of u or when u is the zero vector.
Suppose a 6 × 8 coefficient matrix for a system has six pivot columns. is the system consistent? Why or why not? Choose the correct answer below. There is at least one row of the coefficient matrix that does not have a pivot position. This means the augmented matrix, which will have nine columns, could have a row of the form [0 0 0 0 0 0 0 0 1], so the system could be inconsistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have seven columns and will not have a row of the form [0 0 0 0 0 0 1], so the system is consistent. There is a pivot position in each row of the coefficient matrix. The augmented matrix will have nine columns and will not have a row of the form 0 0 0 0 0 0 0 0 1], so the system is consistent.
Determine if b is a linear combination of a1,a2 and a3. a1 = [2 0 2], a2 = [-4 3 -4], a3 = [-5 8 4], b = [13 -4 9 ] Choose the correct answer below. A. Vector b is a linear combination of a1, a2 and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the third column. B. Vector b is not a linear combination of a1, a2 and a3. C. Vector b is a linear combination of a1, a2 and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column and the third entry in the second column, and the third entry in the third column. D. Vector b is a linear combination of a1, a2 and a3. The pivots in the corresponding echelon matrix are in the first entry in the first column, the second entry in the second column, and the third entry in the fourth column.