Problem 1. Determine if each of the following statements is true or false. Supporting work is not required. Let T : R* → R³ be a surjective linear transformation. Let A be the matrix corresponding to T. Then rankA = 3. True False There exists a 4 x 5 matrix A satisfying rankA = nullityA. True False Let A be a matrix, and B,C be two (arbitrary) echelon forms of A. Then det B = det C. %3D True False | Let A be a n x n matrix such that A2021 = A. If v is an eigenvector of A, then v is an eigenvector of A2021. True False Let A be a n x n matrix. Suppose that A has n distinct eigenvalues, then A is diagonalizable. True False

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Q: Find the standard matrix of a linear transformation T: R³ R4 given by the formula -x₁ + x₂ + x3 3x1…

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Q: 1. For the following linear transformation, T, malo nins W1 = 3x1- 6xX2+ 2x3 w2 = -2x1 + 4x2 + x3 W3…

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Q: Find the matrix A of the linear transformation from R² to R³ given by T([2]) = 4-88 A = 91 +5

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Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.