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For problem 1-5, determine the null space of
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EBK DIFFERENTIAL EQUATIONS AND LINEAR A
- Solve each of the following equations by finding [ a ]1 and using the result in Exercise 9. a.[ 4 ][ x ]=[ 5 ]in13b.[ 8 ][ x ]=[ 7 ]in11c.[ 7 ][ x ]=[ 11 ]in12d.[ 8 ][ x ]=[ 11 ]in15e.[ 9 ][ x ]=[ 14 ]in20f.[ 8 ][ x ]=[ 15 ]in27g.[ 6 ][ x ]=[ 5 ]in319h.[ 9 ][ x ]=[ 8 ]in242 Let [ a ] be an element of n that has a multiplicative inverse [ a ]1 in n. Prove that [ x ]=[ a ]1[ b ] is the unique solution in n to the equation [ a ][ x ]=[ b ].arrow_forwardSuppose that x and y are real numbers such that y is 6 greater than x. What is the smallest possible valueof the product xy?arrow_forwardFind the canonic analytical expression of the following quadratic form q: R³ → R, q (x) = 6x,+x,? – 4x3? + 4x, x3 + 4x, X2, x = (x1, X2, X3) E R³ and the basis relative to this canonic expression. -arrow_forward
- [3.3] Show that (C,+) and (R2, +) are isomorphic.arrow_forward2. Determine the greatest common divisor of a(x) = x³ – 2 and b(x) = x +1 in Q[x] and write it as a linear combination, in Q[x], of a(x) and b(x).arrow_forwardIf zz = -4 + j5, z2 = 3 - j2 , and z3 = 2 - j3 , what is Im (z; - 21) + 2; ? Note: 2* is the complex conjugate of z. Im (z) is the imaginary part of z O 1+ j2 O 11 + j2 none of the choices O -5+ j2arrow_forward
- This is a question from a linear algebra course: Let V = R[X]3, the polynomials of degree at most three, and B = {1, X, X2, X3}. Show what the image under fB is of:• the four basic elements: P1(X) = 1, P2(X) = X, P3(X) = X2 and P4(X) = X3• P(X) = 2 + 6X + 3X2 + 4X3arrow_forwardLet P0" (x) denote the quadratic polynomial that interpolates the data {(xo, yo), (x1, yı), (x2, y2)}; let P"."(x) denote the quadratic polynomial that interpolates the data {(x1, yı), (x2, y2), (x3, Y3)}. Finally, let P3(x) de- note the cubic polynomial interpolating the data{(xo, yo), (x1, yı), (x2, y2), (x3, y3)}. Show that 14. (a) (x3 – x)P0.2) (x) + (x – xo) P!.3) (x) P3 (x) = (1,3) X3 - Xo How might this be generalized to constructing P(x), interpolating {(xo, yo), (Xn, Yn)}, from interpolation polynomials of degreen – 1? (b) ....arrow_forward(3.2) #4iarrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage LearningAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageElements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,