Determine whether the statement below is true or false. Justify the answer. Assume all vectors and subspaces are in R". If an nxp matrix U has orthonormal columns, then UUTX= x for all x in R". Let W be the subspace spanned by the columns of U. Then UTUX = projwyx. If p = n, then W for all x in R". If p

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A: **As per our guidelines we are allowed to answer only one question at a time. Kindly please re-post…

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Q: 4. Orthonormalize S (Gram-Schmidt). 5. Find the projection of v onto W.

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A: As per policy I can solve only one question. Please repost other question.

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A: That's easy. Have a good day!!!

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A: solve the following

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Q: 9

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Q: ) Find a linearly independent set of vectors that spans the same subspace of IR" as that spanned by…

A: First we need to write given vectors in matrix form and try to use row reduced echelon form(RREF) :

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Q: Consider the vector subspaces U, V  ,W ⊆ Rn such that U ⊆ V ⊆ W. If dimU = 5 and dimW = 7, what can…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.