4 - 16 strict a 2x2 matrix B such tha Lota = - 4. - 16). Construct a 2 . Construct a 2 x 2 matrix B such that AB is the zero matrix. Use two different nonzero columns for B. -2 81 B=0
[ 1 - 2. [20 points] Let A = 2. Construct a 2x2 matrix B (not the zero matrix) such that AB = 0. Show that the found matrix does work. 1-2 6
Construct a nonzero matrix B such that AB is the zero matrix. Explain and justify your process. A= 2 5 -3 -1 0-1 3 2 1
Let A be an 3 x 4 matrix, and B an 4 x 3 matrix. Prove: If AB Is, then the columns of B are linearly independent. Let A be an 3 x 4 matrix, and B an 4 x 3 matrix. Prove: If AB Is, then the columns of B are linearly independent.
Suppose A and B are matrices with matrix product AB. If bi, b2, ..., br are the columns of B, then Ab, Ab2, ..., Ab, are the columns of AB 1. Suppose A is an nxnmatrix such that A -SDS where D diag(di,d2,... dn) is a diagonal matrix, and S is an invertible matrix. Prove that the columns of S are eigenvectors of A with corresponding eigenvalues being the diagonal entries of D Before proving this, work through the following...
Let A be a 5 x 3 matrix whose columns are linearly independent. Prove: If B is an invertible 3 x 3 matrix, then the columns of AB are linearly independent. Let A be a 5 x 3 matrix whose columns are linearly independent. Prove: If B is an invertible 3 x 3 matrix, then the columns of AB are linearly independent.
2. Let A be any matrix and let B= AAT a. Use a 2x2 matrix A, to verify that B is symmetric. b. Write one-line proof to show that B is symmetric. Do not use part a. 3. Using Gaussian Elimination, solve the homogeneous system 2x1 + x2 – 3x3 = 0 - x2 - 4x2 + 3x3 = 0 2 1 -3 oli +3707 1-4 3lol 1-4 30
Let A = Construct a 4x2 matrix D, using only 1 and 0 as entries, such that AD = I2. Is it possible that CA =I4 for some 4X2 matrix C? Explain. Is it possible that CA = I4 for some 4 x 2 matrix C? Explain. Choose the correct answer below. A. No, because neither C nor A are invertible. When writing lm as the product of two matrices, since lm is invertible, those two matrices will also be invertible. B. Yes, because...
Construct a 3 x 3 matrix A, with nonzero entries, and a vector b in R such that b is not in the set spanned by the columns of A. Choose the correct answer below. 111 O A. A= 2 2 2 b= 2 (3 4 5] [111] OC. A= 2 2 2 b= (3 3 3] 123] [3 OB. A = 2 1 1 = 2 ( 3 3 2] [1 [111] [4 OD. A = 2 2 2...
1. Find a 2x2 matrix A if for the vector v = 3). Av = [4 +311 I 2. For this problem, use matrices A = and C = matrices A and B commute (so AB=BA) and the matrices A and C commute. Find the entries for the matrix A.