Define the term \"linearly independent\". Find a nonzero vector orthogonal to bo

Question

Define the term "linearly independent". Find a nonzero vector orthogonal to both and . For problems 9 through 14, answer "True" or "False". If A is a 3 times 3 matrix with determinant 3, then the determinant of 2A is 6. When testing a hypothesis about the standard deviation of a normal population, we should use the t-distribution when the sample size is less than 30. If x is an eigenvector for a matrix A, then so is 2x. Two vectors in R^3 are orthogonal if their cross product is 0. If we reject a hypothesis at a .01 level of significance, then we must also reject it at a .05 level of significance.

Explanation / Answer

Dear student, I am only answering the first question as per Chegg Guidelines.

7. "Linearly independent" means that there is no linear relationship between the two variables of concern.In the theory of vector spaces, a set of vectors is said to be linearly dependent if one of the vectors in the set can be defined as a linear combination of the others; if no vector in the set can be written in this way, then the vectors are said to be linearly independent.

no variable can be written as a linear combination of any other variable.

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