4) Find a vector, whose image under T defined by T(X) =Ax, is band determine Wheater x is unique. Let A= 1 4 3 16 0 -3 97 31 1 -13 -28. 17 b==63 3 L-54 Find a single rector x whose image under Tis b x=2 A.) Yes, No free variable B.) No is utree varinbie free vurinbles C.) yes, is D) No, ure no free variable.

Q: O Let ref(Al=Bmrz0 (2 20 X20 where dij = 10 for all i,5 - which is a True state ment? a) (A,Aay-,…

A: If a matrix is of reduced row-echelon form then it is an identity matrix with linearly independent…

Q: a = (-2,4), b = (-1,2), what's the projection of a on b?

A: We know that the formula projection of A on B is  (A.B)/|B|

Q: 8. Given u = (1, 3, 2) and v = (3, 2, 4), find a) u + 2v b) ||u-v|| c) vector w if u + 2w = v

A:

Q: التاريخ 5.1 1 1 If the vector [42] An with the straight Piecel the end point?

A:

Q: letu= 43,5> Let V: L5,2> compute: a) proju u 5.) write u -w, +w,, where Wq is parallel to v and We…

A:

Q: 28. Find the unit vector in the opposite direction to 7 –j + k.

A: We will solve the following

Q: Find 2 × 2 matrices A and B such that т 6 ]A+[, -1 JA+I 5 -5 ]B = [ 4 -6. ] and -2 -1 4 0 -2 -4 3 -4…

A: Given: The equations  06-1-1A+5-534B=4-60-2T0-211A+-4-8-3-6B=3-47-3T

Q: Find the standart devition. Standart sapmayı bulunuz.     A) 7,39 B) 14,78 C) 54,64 D)…

A: Standard deviation= √(summation fiXi2)/n - {(summation fiXi)/n}^2 n= summation fi = (30+40+60+30+25)…

Q: 13.) Find band c so that (5,6,C) is orthogonal to both (1,2,3) с and (1, -2,1)

A:

Q: Sind unit vector Lor 3atb if a-2i4jtk ちのi-25-sk

A: First calculate the vector 3a + b and than devide it with its magnitude for unit vector.

Q: 2] -1 1] a. Find SVD from A 1. A = [4 | b. Find SVD from A invers 2. A = [; : : 8] 1 0 0 0 a. Find…

A:

Q: show all th work with correct ans

A: Solution attached.Explanation:Step 1:Step 2:Step 3:Step 4:

Q: as the sum of two orthogonal orthogonal to ư

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Q: Find the component o7 Position vector of the incenter o7 a triangle having vertices Pi Cl.-l,2),…

A:

Q: 2/Express each vector in the Foim V-v,i+V, jt V, Kk ,2) 12 PiP, if P, is Hhe point cl,2,0) and p ig…

A:

Q: 4. Cuusider the vectors u20 Y 3, 4), w-i+9j, and x N-h A. Find h. l'ind u L. Find wN

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Q: 8. Which line does not lie on the plane r = (1,5,0) + s(2,-3,1)+t(1,−1,4), s,t € R? a. V = (1,5,0) +…

A: To Find: Which of the given lines does not lie on the plane r = (1,5,0)+s(2,-3,1)+t(1,-1,4) where…

Q: a) à = [ 7₁ -2], 6 = [2, -5] b) c = [ 3,5], j = [1, 2]

A:

Q: 2. 9) is = 1 claim T= {A, B, C } O {[:] [:] [:]} A 13 C Pr 2. b) set C₁ linearly c) In A S = Sa…

A:

Q: Find the resaltant vector of the following using graph cal and analntical I=15km 40° East of sonth…

A: Given that T = 15km 40 degree East of South u = 25km 20 degree North-East P = 30km 15 degree West of…

Q: If A-(rsinOcos -cos2Osin

A: Given, At the point , we have determine the vector component of that is parallel to vector .

Q: A linear map T : Rª → R³ is determined by: T(u₁)=v₁, T(u₂)=2v₂, T(U3)= T(u4) = 0, (c) Give the…

A:

Q: Qzi In Vu CR) it u =(\,-1,\,-1), v = (- 2,2,-2, 2) Find iI lull and l vl)

A: Consider the given vectors as, u=1,-1,1,-1 and v=-2, 2,-2, 2 If vector u=a,b,c,d then u=a2+b2+c+d2…

Q: Consider a dihedral groop Dy=<agb: asb= (abj=1 Ds cuss all Dy and verify Subgooups of "Dy=…

A: See answer below.

Q: 2. The position vectors of A, B and C relative to a fixed origin O are respectively, Find, ABAC

A: [2].

Q: 3. Show that if I aij = 1, then if A= (orj), entrees of of then the sum of vector V Av equals the…

A:

Q: 025 of Axco Descube el salutons l salutions Vectare form where A is Yow eluivelent falom to the…

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Q: 2.Let a = (2,3,5) and uz(-,2,3) be Vecters in IR?. a) Find the rector Component Of u along a. 6)…

A: The vector component of u along a is also called the projection of u on a.

Q: Q8) The planes 3x+6z=1 and .2x+2y-z=3 are orthogonal F O

A:

Q: A vector v is defined with initial point P = (2, -6) and terminal point Q = (-3, -2) a)  Graph the…

A: Given  A vector v is defined with initial point P = (2, -6)  terminal point Q = (-3, -2)

Q: 10. Determine whether the given vectors are in span S = G -CHEED (i a) b)

A:

Q: 5. Given three vectors , U V and W u+2v+w=0_and_u•v=3. If ||ū||=||||=2, find . such that

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Q: and the projection pros

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Q: llelpped

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Q: 3) of a) rotation b) Confider each. c) reflection Projection let • maps Linear • thon' I T matrix be…

A: To Find: Matrix representation of transformation: (a) That represents rotation of angle 30°. (b)…

Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=&lt;2,-2,1&gt;.

Q: Consider ỹ,,y2, ÿ,ER³ and that y,+y,+y;=0. For Î=span{ ỹ,,y} and Y=span{ỹ2, y, show that Î=Ỹ.

A: Given  that  y→1, y→2, y→3∈ℝ5 and that                   y→1+ y→2+ y→3=0→. and           Y^=spany→1,…