Give bases for row(A), col(A), and null(A).row(A)col(A)null(A)2-4 2012 1 2 11-2 3 2 20000000

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Answered: Give bases for row(A), col(A), and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Use the fact that matrices A and B are row-equivalent. -2 -5 8 0 -17 1 -5 1 5 A = -5 -11 17 3 -53 1 7 -13 5 -3 1 0 1 0 0 1 -2 0 3 B = 0 0 0 1 -5 0 0 0 0 3.
(Left nullspace) Add the extra column b and reduce A to echelon form: [1 2 3 [Ab] 4 5 6 bi 1 b₂ → 2 3 0-3 -6 7 8 9 b3 0 00 bi b2-4b₁ b3 - 2b2 + b₁ A combination of the rows of A has produced the zero row. What combination is it? (Look at b3 - 2b2+ b₁ on the right side.) Which vectors are in the nullspace of AT and which vectors are in the nullspace of A?
b1 = ______ b2 = ______
Find the matrix of the quadratic form 2x1? + 3x2² – x32 + 4x1x2 – 2 x1x3 + 6x2x3 2 2 -2 1 (a) 2 3 (b) -2 3 3 -1 3 -1 1 3 -1 2 -2 -1] [2 2 1 (d) 2 l1 -2 3 3 3 -3 [-1 3 -1. -3 -1.
If a and B are constructible, then (a) is constructible.
III. Used series of Elementary Row/Column Operations transform matrix given below into Row-Echelon Form (REF) or Reduced Row-Echelon Form (RREF). Fill in the blank box with the elementary operations for the given step and the corresponding result matrix. Use the word "over" without a space between the numerator and denominator to indicate the fraction bar or vinculum. Also, for the interchange symbol, write the word "interchange" with no spaces between the rows to be exchanged. For example, R2 is written as R2-2R1 R1 is written as (4over3)R1; -R2 is written as (-(1 over2)) R2; and R2-2R1 or -2R1+R2; and R2 R1 is written as R2interchangeR1. 3 [2 8 4 17) 2 14 5 1 5 10 -1 1. Elementary operations Step 1. Step 2. Step 3. Step 4. Step 5. Step 6. Step 7. Step 8. Step 9. Resulting Matrix UU OOL
Let u = -7 5 -6 , V = -7 7 equation 5-2 -6 6 7 -2 6 X₁ x2 X₁ X2 (Simplify your answers.) and w= - 14 -11 - 12 - 14 - 11 . It can be shown that -5u-7v-w=0. Use this fact (and no row operations) to find x₁ and x₂ that satisfy the - 12
Which of the following statements is true about the Elementary row operations O We can multiply any row by a non-zero constant/ O We can add a multiple of a column to a row OWe can interchange any two columns. O we can multiply any column by an non-zero constant

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Give bases for row(A), col(A), and null(A). row(A) col(A) null(A) 2-4 201 2 1 2 1 1-2 3 2 2 000 0000