For each statement, indicate whether it's true or false. For the ones that are false, state the correct true statement. а. Not every linearly independent set in R" is an orthogonal set. b. If y is a linear combination of nonzero vectors from an orthogonal set, then the weights in the linear combination can be computed without row operations on a matrix. If the vectors in an orthogonal set are normalized, then some of the new vectors may not be orthogonal. с. d. If the columns of an mxn matrix A are orthonormal, then the linear mapping i→ Ax preserves lengths. An orthogonal matrix is invertible. е.

2.10 If A, B, and C are noncoplanar vectors (that is, A, B, and C are linearly independent), determine if the following set of vectors is linearly independent: r₁ = A- 3B +2C, r₂ = 2A-5B +3C, r3 = A - 5B + 4C.

Determine whether the set of vectors is orthonormal. If the set is only orthogonal, normalize the vectors to produce an orthonormal set. u₁ 5 H and U₂ = 0 1 5 3 2|2 Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. OA. The set of vectors is orthogonal only. The normalized vectors for u, and u₂ are (Type exact answers, using radicals as needed.) OB. The set of vectors is orthonormal. OC. The set of vectors is not orthogonal. and respectively.

Let u be a vector that is not a linear combination of {u₁, U₂, U3, }. Select the best statement. A. span{u₁, U₂, U3 } = span{U₁, U₂, U3, U4 } . B. We only know that span{u₁, U₂, U3} C span{U₁, U₂, U3, U4 } . C. There is no obvious relationship between span{u₁, U₂, U3} and span{u₁, U2, U3, U4}. D. span {u₁, U₂, U3} = span{u₁, U₂, U3, U4} when none of {u₁, U₂, U3, } is a linear combination of the others. E. span{u₁, U₂, U3} is a proper subset of span{u₁, U₂, U3, U4 } . F. We only know that span{u₁, U2, U3, U4} C span{u₁, U₂, U3} . G. none of the above