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For problem 1-5, determine the null space of
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Differential Equations and Linear Algebra (4th Edition)
- 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_forwardShow that P(x)=2x39x2+7x+6 has at least one real zero between 1and0.arrow_forwardThe sum of two positive real numbers x and y is 3. Find an x and y among these such that the product xy² is maximal. X = y =arrow_forward
- Suppose (x1,x2) + (Y1,Y2) is defined to be (x1 + Y2 ,x2 + Y1). With the usual multiplication cx = ( cx1, cx2 ), which of the eight conditions are not satisfied?arrow_forwardQuestion 2: For which real values of a do the polynomials PA(t) = at? -글t-글 P2(t) = -글2 + at-글 Pa(t) =D -글: Pa(t) %=D - 2-글+a form a linearly dependent set in P2?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_forward
- 7. The two quadratic relations intersect at 2 points, points A and B. Determine graphically the coordinates of each of the points of intersection. O y (х-1)(х—9) 2 10 ТУ 2- -10-8-6 -4-2 -2+ 4 8 10 -4 -81 -10 1 1 39 4 4 XT do ||arrow_forwardFind the null space for A. - [1 null(A) A = 15-5 0 1 -³] 3 = spanarrow_forwardShow that ℝ3 = span( 1 1 2 1 2 1 0 3 -1arrow_forward
- Find AB such that [3 1 21 T-1 A = 2 1 2 and B =|4 [1 2 2] -2 -5]arrow_forward3. Let a ER and let: 1 -2 2 4- ( -² ) A = 1+ a 4+ a -2. a " a a 2 - a You may assume without calculation that ch₁(x) = (x − 2)²(x − 3). For which values of a, is A diagonalisable?arrow_forward(Q. +..) is a subfield of (F = {a+ bV5: a, b e Q}, +, .): W (F = {a+ bv5: a, be Q}, +,.) is a subfield of (IR, +,.); (3) %3D (4) %3Darrow_forward
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