please answer both questions thank you! How many rows and columns must a matrix A have...
Compute the product using (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights, and (b) the row-vector rule for computing Ax. If a product is undefined, explain why. 1 2 - 3 -3 1 1 3 (a) Set up the linear combination of the columns of A using the corresponding entries in x as weights. Select the correct choice below and, if necessary, fill in any answer...
Find all x in R that are mapped into the zero vector by the transformation x Ax for the given matrix A. 111 13 A 0 1-4 4 4 -16 28-36 Select the correct choice below and fill in the answer box(es) to complete your choice. O A. There is only one vector, which is x- + X 3
Explain why the columns of an nxn matrix A are linearly independent when A is invertible Choose the correct answer below. O A. IFA is invertible, then for all x there is a b such that Ax=b. Since x = 0 is a solution of Ax0, the columns of A must be linearly independent OB. IA is invertible, then A has an inverse matrix A Since AA A AA must have linearly independent columns O C. If A is invertible,...
6 3 Compute the product using the methods below. If a product is undefined, explain why. a. The definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights. b. The row-vector rule for computing Ax. 2 - 5 -4 -5 7 4 a. Set up the linear combination of the columns of A using the corresponding entries in x as weights. Select the correct choice below and, if necessary, fill...
Problem 4. How many pivot columns must a 10 ~ 8 matrix have if its columns are linearly independent? Justify your answer. Problem 5. How many pivot columns must a 5 x 8 matrix have if its columns span R5? Justify your answer.
Determine if the columns of the matrix form a linearly independent set. Justify your answer. -2 -1 01 0 - 1 3 1 1 -6 2 1 - 12 Select the correct choice below and fill in the answer box within your choice. (Type an integer or simplified fraction for each matrix element.) O A. If A is the given matrix, then the augmented matrix represents the equation Ax = 0. The reduced echelon form of this matrix indicates that...
1 7 -6 13 Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= -2 -5 3 b= -8 ܗ - 4 - 6 -2 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within...
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...
Determine if y is in the subspace of R4 spanned by the columns of A. -7 w 9 6-7 T-9-9 3 | 10 -2 -8 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. O A. The vector y is in the subspace spanned by the columns of A because y can be written as a linear combination of these columns as follows. (Type integers or simplified fractions.) OB. The vector y...
a. Every matrix equation Ax b corresponds to a vector equation with the same solution set. Choose the correct answer below. O A. False. The matrix equation Ax-b does not correspond to a vector equation with the same solution set. O B. False. The matrix equation Ax b only corresponds to an inconsistent system of vector equations. O c. True. The matrix equation Ax-bis simply another notation for the vector equation x1a1 + x2a2 +·.. + xnan-b, where al ,...