Let A and B be two 3 x 3 invertible matrices, and let u, 7, w€ R³ be column vectors. Recall that for a matrix B we let TB denote its corresponding matrix transformation. Look at the expressions that follow. Select the ones that DO NOT make sense, because they either equate two different "types" of thing that can't be equal or try to perform an operation that is not defined. (For the computer programmers reading this, the question is essentially "find the type errors".) Notation clarification: Any time you see the symbol it denotes the dot product, and any time you see the symbol x it denotes the cross product Warning: To clarify, you're not being asked which ones are true. You're being asked to identify which equations don't make sense. From the 13 choices, select all that apply VA u x (v.w) (v. u) A (TA-1)-¹ = A-¹ v.v=ux v (v. u) A(v × ū) (TA-¹)¹=TA Av ATA = A úxv=uv (u xv). w A =TA A(v x u)
Let A and B be two 3 x 3 invertible matrices, and let u, 7, w€ R³ be column vectors. Recall that for a matrix B we let TB denote its corresponding matrix transformation. Look at the expressions that follow. Select the ones that DO NOT make sense, because they either equate two different "types" of thing that can't be equal or try to perform an operation that is not defined. (For the computer programmers reading this, the question is essentially "find the type errors".) Notation clarification: Any time you see the symbol it denotes the dot product, and any time you see the symbol x it denotes the cross product Warning: To clarify, you're not being asked which ones are true. You're being asked to identify which equations don't make sense. From the 13 choices, select all that apply VA u x (v.w) (v. u) A (TA-1)-¹ = A-¹ v.v=ux v (v. u) A(v × ū) (TA-¹)¹=TA Av ATA = A úxv=uv (u xv). w A =TA A(v x u)
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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Transcribed Image Text:Let A and B be two 3 x 3 invertible matrices, and let u, v, w € R³ be column vectors.
Recall that for a matrix B we let TB denote its corresponding matrix transformation.
Look at the expressions that follow. Select the ones that DO NOT make sense, because they either equate two different "types" of thing that can't be
equal or try to perform an operation that is not defined. (For the computer programmers reading this, the question is essentially "find the type erro
errors".)
Notation clarification: Any time you see the symbol it denotes the dot product, and any time you see the symbol x it denotes the cross product
Warning: To clarify, you're not being asked which ones are true. You're being asked to identify which equations don't make sense.
From the 13 choices, select all that apply
VA ũ × (v · w) (õ · ū)A
.
(TA-1)-¹ = A-¹
v.v=ux v
(v. ū) A (v × ū)
(TA-¹)−¹ = TA
Αὖ
ATA
= A
u x v = uv
(ũ × v) • w
A =TA
A(v × ū)
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