Let L be a linear operator on Rn. Suppose that L (x) = 0 for some x ≠ 0. Let A be the matrix representing L with respect to the standard basis {e1, e2, . . . , en}. Show that A is singular.

Q: Find the coordinate matrix of x in Rn relative to the basis B'. B' = {(4, 3, 3), (-11, 0, 11), (0,…

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Q: Define a linear operator (transformation) on R2 by performing the following operations in order: (i)…

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Q: Let A be an nxn matrix. Prove that dim(col(A²)) < dim(col(A)).

A: Given: Assume that, A is an n×n matrix.

Q: be the bases in  R³ T={,,},     S={,,} determine the matrix of transicion of T to S

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Q: 10 3. Find 3⁰⁰ mod 7, /0 5 mod 11

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Q: 9. Consider the following 2 x 2 matrix A and basis S of R²: = [] and 5 = {[¹²₂] [²³₂]} The matrix A…

A: Given linear operator A=2456     and  basis   S= 1-2  ,3-7

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.