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Let T be a linear transformation from R³ into R³. Find T-1 T(X1₁X₂₁X3) = (X₁ + X3, X₁ −X₂ + X3, X₁ + 2x₂+2x3) a. b. T(X₁,×2,×3)=—=—(2×₁+X2−X×3₁ −3×₁+6×₂-X3₁ −X₁+2×₂-2x3) T(x₁1x₂x3) = (2x₁ + x₂-2X3, X₂-X3, c. T(x1x₂x3) = (2x₁ + x₂-2X3, X₂ X3 d. T(x1,x2x3) = (4x₁-2x₂-X3, X₁-X₂, X₁ + X3) X₁ + X3) 1 3X₁ + 2x₂ + x3) e. T(×₁,×2,×3)==-(-x₁+3x₂+3x3, −3x₁-x₂ + 4x3,2x₁-x₂ −X3)

Let T be a linear transformation from R³ into R³. Find T-1 T(X1₁X₂₁X3) = (X₁ + X3, X₁ −X₂ + X3, X₁ + 2x₂+2x3) a. b. T(X₁,×2,×3)=—=—(2×₁+X2−X×3₁ −3×₁+6×₂-X3₁ −X₁+2×₂-2x3) T(x₁1x₂x3) = (2x₁ + x₂-2X3, X₂-X3, c. T(x1x₂x3) = (2x₁ + x₂-2X3, X₂ X3 d. T(x1,x2x3) = (4x₁-2x₂-X3, X₁-X₂, X₁ + X3) X₁ + X3) 1 3X₁ + 2x₂ + x3) e. T(×₁,×2,×3)==-(-x₁+3x₂+3x3, −3x₁-x₂ + 4x3,2x₁-x₂ −X3)

Advanced Engineering Mathematics
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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Let T be a linear transformation from R³ into R³. Find T-1 T(X1₂X2₂X3)=(X₁ + X3, X₁−X₂ + X3, X₁ + 2x₂ + 2x3) a. T(×₁,×2,×3)=—=—(2×₁+x₂−X3₁ −3×₁+6×₂-X3₁ −X₁+2x₂-2x3) b. T(x1x₂x3) = (2x₁ + x₂-2X3, X₂ X3, X1 + X3) X1 + X3) c. T(x1,x2x3) = (2x₁ + x₂ -2X3, X₂ X3 d. T(x₁,x₂,X3)= (4x₁-2×₂-X3, X₁-X₂, 3X₁ + 2x₂ + x3) T(X1₁X₁₁X3)= (-X₁+3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ −x₂ −X3)
Transcribed Image Text:Let T be a linear transformation from R³ into R³. Find T-1 T(X1₂X2₂X3)=(X₁ + X3, X₁−X₂ + X3, X₁ + 2x₂ + 2x3) a. T(×₁,×2,×3)=—=—(2×₁+x₂−X3₁ −3×₁+6×₂-X3₁ −X₁+2x₂-2x3) b. T(x1x₂x3) = (2x₁ + x₂-2X3, X₂ X3, X1 + X3) X1 + X3) c. T(x1,x2x3) = (2x₁ + x₂ -2X3, X₂ X3 d. T(x₁,x₂,X3)= (4x₁-2×₂-X3, X₁-X₂, 3X₁ + 2x₂ + x3) T(X1₁X₁₁X3)= (-X₁+3x₂ + 3x3, −3x₁-x₂ + 4x3,2x₁ −x₂ −X3)
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