If it holds that for a nonempty collection of vectors X := \{x_1,\ldots, x_K\} \subset \mathbb{R}^N \sum_{k=1}^K \alpha_k x_k = 0 \; \Rightarrow \; \alpha_1 = \cdots = \alpha_K = 0, they are called [missing word 1] [missing word 2]. Write the first missing word简答题

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Question29 Consider the functions [math] and [math]. Use the Wronskian to decide whether these functions are linearly independent on the interval [math]. Which of the following gives the correct answer and appropriate justification for it? Select one alternative: [math] has nonzero determinant for every value of [math], so the functions are linearly independent. [math]has determinant equal to zero for every value of [math], so the functions are linearly independent. [math]has determinant equal to zero for every value of [math], so the functions are linearly dependent. [math]has nonzero determinant for every value of [math], so the functions are linearly dependent. ResetMaximum marks: 1 Flag question undefined

Which of the following statements are true? Statement A:  The set of functions   { 𝑒 𝑡 , 𝑒 2 𝑡 }  is linearly independent on  𝑅 . Statement B:  The set of functions   { sin ⁡ ( 3 𝑡 ) , cos ⁡ ( 3 𝑡 ) }  is linearly dependent on  ( 0 , 2 𝜋 ) . Statement C:  The set of functions   { 1 , 𝑡 2 }  is linearly independent on  𝑅 .

Which of the following statements are true? Statement A:  The set of functions  {et,e2t}  is linearly independent on  R. Statement B:  The set of functions  {sin(3t),cos(3t)}  is linearly dependent on  (0,2π). Statement C:  The set of functions  {1,t2}  is linearly independent on  R.

Section A: Read the text and answer the questions. Brutalism is an architectural style, introduced in the 1950s. It uses exposed concrete to create geometric structures with a grey appearance. Concrete buildings are often criticised as cold and ugly, lacking the warmth of stone or the smooth feel of steel. However, concrete, as a building material, has unique characteristics. It is extremely flexible when wet, and is adapted to create interesting shapes. Many urban public buildings, such as universities, have also used concrete as the main material to indicate strength and permanence. Instead of keeping Brutalist buildings, many are being demolished to make space for modern styles. However, this does not acknowledge the cultural history of these buildings, and is not sustainable. Fill in the gap with ONE WORD from the paragraph. 1. Brutalist architecture included exposed concrete, which gave a cold Answer Question 1[input] .

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