Using MATLAB to Decide Linear Dependence Sargam that en rani la are linearly dependent. After type 5.A In MATLAR the Smuts A ly typing These from MATLAB -0.7699 - 3780 0.3760 0.3700 will not only suming the term atas - irat train lude this with that we can make we 4 144 144 #4 444 44s got hurt the status (2 and 2) to obtain optymati 3-0 showing that the only on the They expedient. For the part was of the final impedit. 1. It w levetit in the water spore Vse that the sets of vectors (0,0) auto--) are lydende 2. For wide values are the victim al-1) independent -=(-1.1) * =121.-2)=(102-6) Is the www} linearly birto lyhyet? 3. 5. Show that the poli+ly indeed Using MATLAB to Decide Linear Dependence Suppose that we want to determine whether or not the vectors 1 0 2 1 4 4 wa -1 04 3 3 -2 5 3 12 1 -2 are linearly dependent. After typing e5.4.4 in MATLAB, form the 5 x 4 matrix A by typing 186 A - [wi w2 w3w4] Determine whether there is a nonzero solution to AR = 0 by typing null(A) The response from MATLAB is ans = -0.7559 -0.3780 0.3780 0.3780 null(4), anot empty A- = [w1 W2 w3 w4) Determine whether there is a nonzero solution to AR=0 by typing null(A) The response from MATLAB is ans = -0.7559 -0.3780 0.3780 0.3780 null(A), is not empty showing that there is a nonzero solution to AR O and the vectors w; are linearly dependent. Indeed, this solution for R shows that we can solve for w in terms of w2, w3, 4. We can now ask whether or not. are linearly dependent. To answer this question form the matrix B = [w2 w3 w4] and type null(B) to obtain ans = Empty matrix: 3-by-o showing that the only solution to BR = 0 is the zero solution R = 0. Thus, u, ws. We are linearly independent. For these particular vectors. any three of the four are linearly independent. Using MATLAB to Decide Linear Dependence Sargam that en rani la are linearly dependent. After type 5.A In MATLAR the Smuts A ly typing These from MATLAB -0.7699 - 3780 0.3760 0.3700 will not only suming the term atas - irat train lude this with that we can make we 4 144 144 #4 444 44s got hurt the status (2 and 2) to obtain optymati 3-0 showing that the only on the They expedient. For the part was of the final impedit. 1. It w levetit in the water spore Vse that the sets of vectors (0,0) auto--) are lydende 2. For wide values are the victim al-1) independent -=(-1.1) * =121.-2)=(102-6) Is the www} linearly birto lyhyet? 3. 5. Show that the poli+ly indeed Using MATLAB to Decide Linear Dependence Suppose that we want to determine whether or not the vectors 1 0 2 1 4 4 wa -1 04 3 3 -2 5 3 12 1 -2 are linearly dependent. After typing e5.4.4 in MATLAB, form the 5 x 4 matrix A by typing 186 A - [wi w2 w3w4] Determine whether there is a nonzero solution to AR = 0 by typing null(A) The response from MATLAB is ans = -0.7559 -0.3780 0.3780 0.3780 null(4), anot empty A- = [w1 W2 w3 w4) Determine whether there is a nonzero solution to AR=0 by typing null(A) The response from MATLAB is ans = -0.7559 -0.3780 0.3780 0.3780 null(A), is not empty showing that there is a nonzero solution to AR O and the vectors w; are linearly dependent. Indeed, this solution for R shows that we can solve for w in terms of w2, w3, 4. We can now ask whether or not. are linearly dependent. To answer this question form the matrix B = [w2 w3 w4] and type null(B) to obtain ans = Empty matrix: 3-by-o showing that the only solution to BR = 0 is the zero solution R = 0. Thus, u, ws. We are linearly independent. For these particular vectors. any three of the four are linearly independent
