1 1 2 Let A = 3 1 0 -4 1 1.1 Find a basis B1 for im(A), and a basis B2 for null(A). 1.2 Explain briefly why im(A) is a plane, (geometrically and find the equation of this plane. 1.3 Explain (briefly) why null(A) is a line (geometrically) and find the equation of this line.

Q: [4 5 9 -21 1. Consider A = 6 5 3 4 8 1. 12 -3 (c) What is Col A? (d) Find a basis for Col A. (e)…

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Q: If B={(1,1,1).(1,0,1),(0,1, 1) } is a basis of R3, then the second coordinate of the vector (3.5.7)…

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Q: (b) The general fact that fcu++eUn]e== c\]j + .. + ca[vn]s allows for rewriting the equation above…

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Q: 4. Apply the principal axis transformation to the curve of second order -x2 + 6xy – y? – 22.x+ 18y –…

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Q: 1 4 Let S = {v,,v2,v,} where v, = -3 -7 %3D V2 = V3 1 1 3 1 3 a. Explain why the set S is not a…

A: Note: Since you have asked multiple question, we will solve the first question for you. If you want…

Q: 9. Find a basis for the hyperplane a where a-(2, 1. -3).

A: Note: As per bartleby instruction when more than one question is given only one has to be answered.…

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A: Given vector is: Pt=1+3t-6t2 Basis set for the vector is given as: B=1-t2, t-t2, 2-t+t2 Then, let…

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Q: Iif a basis for g2is y3 = { 4 and : 7 2 find the coordinate vector [X] -5 5 3

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Q: Which of the following vectors form an orthogonal basis? 2 [0] T- 1] 3 го а) -1 4 b) -2 3 剛 2 -2' 3…

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Q: 1) Let T a b la + 2b +2c + 1d + 7e+ (-1) f la + 2b + 4c + 4d +21e+(-2)ƒ la + 2b +3c+ 2d + 12e + (-2)…

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Q: Let S = y1 be a basis of R and x = E R4. What are the coordinates of x with %3D >Y2 = respect to the…

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Q: -{{}")} B = 4 -10 is a basis for R². Find the coordinates of the vector x relative to the basis B.…

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Q: 1. In each of parts (a)-(d), determine whether the given vectors form a basis for R?. a) b) -12 9.…

A: Dear Bartleby student, according to our guidelines we can answer only three subparts, or first…

Q: 13 4 Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x is…

A: Given system of equation is  Ax=b, withA=12741030011-4-9-29,  b=13583-55  Now  find the right answer…

Q: 2 3 1 0 1 1 1 1 1 1 Find the coordinate vector of A = with respect to the basis B of M22' 4 5 0 0 1

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Q: -2 1 4 -2 4. Find a basis for H= Span subset of these vectors that spans H. A LE 64 10 N t That is,…

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Q: -3' 2, uz [3] -4 is an orthogonal basis of R3 and x = 2 Let u1 1, u3 4 If x can be expressed as a…

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Q: This doesn't make sense. How does x1-x3=0? shouldn't it be (1,0,0)-(-1,2,-2)=(2,-2,2)? Can you…

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Q: Let ={t?-1, t²-t, -t?+t-2} be a basis for P,(R). Then the coordinates of p(t)=6t2-3t-1 are [p]= %3D

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Q: Do the following vectors form a basis for R? O a. Yes, the vectors form a basis for R2 O b. Cannot…

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Q: {H H} Let B = Note that B is a basis for R2. (You do not need to prove this. (a) Find the…

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A: Consider the matrix A and basis B’.

Q: The vectors p1(t)=1+t?,p2(t)%3Dt-3t2,p3(t)-1+t-3t2 form : B= {P1, P2, P3} for P2(R). Let q(t)=1+3t -…

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Q: 3 2. (а) Do the vectors vị = -1 -1 form a basis for R³? , V3 = 1 > V2 = -I--- (b) Do the vectors vị…

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Q: Suppose S= {Pi;P2•P3;P4,P5;P6} is a basis for P5 and p is a polynomial of degree 4. Then the…

A: Given The coordinate vector is a vector in which each component is the coefficient of the linear…

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Q: [1 1 2] Q1 Let A: 1 2 1, a:-[1,-1,4] and b:= 3 5 4 (a) Show that a E row(A). (b) Show that be…

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Q: -7 -7 The orthogonal basis produced using the Gram-Schmidt process for W is (Use a comma to separate…

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Q: 1 -1 1 Which of the following is a basis of IR*that includes the vectors and 1 1 1 1

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Q: If {e², e-², e2=} is a basis of solutions of y" + ay" + by + cy = 0, then c= (A) -1 (В) -2 (C) 2 (D)…

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Q: 1 -1 4. Find a vector v for which 2 1 is a basis of R³. 3 1 5. Find a vector v for which is not a…

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Q: 2. Give the matrices of the following plane transformations: a)The rotation around the origin of the…

A: (b) Given the horizontal transvection Te2=-3e1+e2. This is followed by a reflection with respect to…

Q: Oa + Ob+0c + 4d la + (-1) b+ (-2) c +4d Oa + 1b + (-2) c + 5d la + (-1) b+ (-2) c + 2d 2a + 1b+…

A: 1) Let Tabcd=0a+0b+0c+4d1a+(-1)b+(-2)c+4d0a+1b+(-2)c+5d1a+(-1)b+(-2)c+2d2a+1b+(-10)c+4d   To Find:…

Q: 1 6 14 8 50 Find a vector x whose image under T, defined by T(x) = Ax, is b, and determine whether x…

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Q: Let s = {(r² –3r+4, 2r-5, x²+1} be a basis for P2, let q E P2. If (q). = [2,-3, 1], then q = %3D %3D…

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Q: - 10 -4 3 1 - 10 8 13 2 Find the QR factorization of A with the given orthogonal basis. An…

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Q: - 10 -7 8 - 1 - 10 3 6 2 8 10 2 3 An orthogonal basis for A, -6 -9 0 - 3 ,is - 6 - 3 6 Find the QR…

A: We have given orthogonal basis for A and we have to find QR factorization of A with the given…

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A: Given space is W=spanv1,v2 where v1=-110 and v2=42-3. (i) Given x=-113. Therefore to find orthogonal…

Q: - 10 - 6 - 10 4 6 18 4 6. An orthogonal basis for A, - 6 - 10 0 . Find the QR factorization of A…

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A: The given vectors are as follows. v1=112-4, v2=231-6, v3=216-10 and w=531-9 If w is a linear…

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Q: -31 Let u1 = 2,Uz [3] 1 U3 is an orthogonal basis of R3 and x = 2 If x can be expressed as a linear…

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Q: 1. Use coordinate vectors to show that (4-t), (3-1), 2-t,and 1+5t-6r +f form a basis for P. Then…

A: To check that the polynomials 4-t3, 3-t2, 2-t, 1+5t-6t2+t3 form a basis for P3. We will write the…

Q: a b 1) Let T cla + 2b + 1c + 3d + (-11) e+ (-la+ (-1) b + (-2) c + Od + 7e) x. d to Then a basis for…

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Q: 2. 5. Consider twO basis of R: B = %3D -3 and (= 3. 5- 1- with respect to B, If a vector V E PR has…

A: The given 2 bases of ℝ2 are as follows. B=75, -3-1 and C=3-5, -12 Also, the coordinates of the…

Q: 2 21 [1] 1 and y = |2 [3. Let u1 = 5 uz and W= Span{u1, U2}. (a) Find an orthogonal basis for W. (b)…

A: Given that, , And, And,…