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3. We want to find a matrix B corresponding to a transformation TB (-) such that TB (TA(x)) = R² and TB (TA (е₁)) = 0 for i=1,2 where e₁,e2, e3 are the canonical basis vectors in R³. What are the dimensions of B (number of rows and columns) 3a. 3b Given the above conditions what are the possible values for rank(B)

3. We want to find a matrix B corresponding to a transformation TB (-) such that TB (TA(x)) = R² and TB (TA (е₁)) = 0 for i=1,2 where e₁,e2, e3 are the canonical basis vectors in R³. What are the dimensions of B (number of rows and columns) 3a. 3b Given the above conditions what are the possible values for rank(B)

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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3. We want to find a matrix \( B \) corresponding to a transformation \( T_B(\cdot) \) such that \( T_B\left(T_A(x)\right) \in \mathbb{R}^2 \) and \( T_B\left(T_A(e_i)\right) = 0 \) for \( i = 1, 2 \) where \( e_1, e_2, e_3 \) are the canonical basis vectors in \( \mathbb{R}^3 \). 3a. What are the dimensions of \( B \) (number of rows and columns)? 3b. Given the above conditions what are the possible values for \(\text{rank}(B)\)?
Transcribed Image Text:3. We want to find a matrix \( B \) corresponding to a transformation \( T_B(\cdot) \) such that \( T_B\left(T_A(x)\right) \in \mathbb{R}^2 \) and \( T_B\left(T_A(e_i)\right) = 0 \) for \( i = 1, 2 \) where \( e_1, e_2, e_3 \) are the canonical basis vectors in \( \mathbb{R}^3 \). 3a. What are the dimensions of \( B \) (number of rows and columns)? 3b. Given the above conditions what are the possible values for \(\text{rank}(B)\)?
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Given : two transformations TA and TB such that TBTAx∈ℝ2 , and TBTAei=0 for i=1,2. where e1,e2,e3 are canonical basis of ℝ3.

3a) To Find: Dimensions of matrix B.

3b) To Find: Possible values for rank of B.

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