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Find all x in R that are mapped into the zero vector by the transformation x...
Linear Transformation
Find all \(x\) in \(R^{4}\) that are mapped into the zero vector by the transformation \(x \mapsto A x\) for the given matrix \(A\).$$ A=\left[\begin{array}{rrrr} 1 & -3 & 6 & 1 \\ 0 & 1 & -5 & 2 \\ 2 & -4 & 2 & 6 \end{array}\right] $$Select the correct choice below and fill in the answer box(es) to complete your choice.
please answer both questions thank you! How many rows and columns must a matrix A have...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
9.4.22 Question Help The given vector functions are solutions to the system x'(t) = Ax(t). 2...
9.4.22 Question Help The given vector functions are solutions to the system x'(t) = Ax(t). 2 6 5t 6t X1 se X2e - Determine whether the vector functions form a fundamental solution set. Select the correct choice below and fill in the answer box(es) to complete your choice. A. No, the vector functions do not form a fundamental solution set because the Wronskian is B. Yes, the vector functions form a fundamental solution set because the Wronskian is The fundamental...
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to...
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to the zero vector by x → Ax. Is the map 16 -2 -5 10] TA(x) = Ax one-to-one (injective)? e le vert is the vector b= 3 in range(TA)? What about c= 13 ? Is L7 sector what aboute=p} L7 Ta onto (surjective)?
Describe the solutions of the first system of equations below in parametric vector form. Provide a...
Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x1 +4x2+8X3 = 16 - 12X1 - 12X2 - 24x3 = - 48 - 6x2 - 6x3 = 18 4x7 +4x2+8X3 = 0 - 12X1 - 12X2 - 24x3 = 0 - 6x2 - 6x3 = 0 X1 Describe the solution set, x = X2 of the first system of equations...
A.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero mat...
a.) if A is an m*n matrix, such that Ax=0 for every vector x in R^n, then A is the m * n Zero matrix b.) The row echelon form of an invertible 3 * 3 matrix is invertible c.) If A is an m*n matrix and the equation Ax=0 has only the trivial solution, then the columns of A are linearly independent. d.) If T is the linear transformation whose standard matrix is an m*n matrix A and the...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined o...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix...
1 7 -6 13 Given A and b to the right, write the augmented matrix for...
1 7 -6 13 Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= -2 -5 3 b= -8 ܗ - 4 - 6 -2 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within...
Compute the product using (a) the definition where Ax is the linear combination of the columns...
Compute the product using (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights, and (b) the row-vector rule for computing Ax. If a product is undefined, explain why. 1 2 - 3 -3 1 1 3 (a) Set up the linear combination of the columns of A using the corresponding entries in x as weights. Select the correct choice below and, if necessary, fill in any answer...
Find g'(x) for the given function. Then find g'(-2), g'(0), and g'(2). g(x) = V7x Find...
Find g'(x) for the given function. Then find g'(-2), g'(0), and g'(2). g(x) = V7x Find g'(x) for the given function. g'(x) = 0 Find g'(-2). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A g'(-2) = (Type an exact answer.) OB. The derivative does not exist. Find g'(0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. g'(0) =...
please answer both questions thank you!
How many rows and columns must a matrix A have in order to define a mapping from R into R by the rule T(x) Ax? Choose the correct answer below OA. The matrix A must have 7 rows and 7 columns. O B. The matrix A must have 9 rows and 7 columns OC. The matrix A must have 9 rows and 9 columns O D. The matrix A must have 7 rows and...
9.4.22 Question Help The given vector functions are solutions to the system x'(t) = Ax(t). 2 6 5t 6t X1 se X2e - Determine whether the vector functions form a fundamental solution set. Select the correct choice below and fill in the answer box(es) to complete your choice. A. No, the vector functions do not form a fundamental solution set because the Wronskian is B. Yes, the vector functions form a fundamental solution set because the Wronskian is The fundamental...
13 -1 -3 61 A= 0 0 -3 6 . Find all the vectors mapped to the zero vector by x → Ax. Is the map 16 -2 -5 10] TA(x) = Ax one-to-one (injective)? e le vert is the vector b= 3 in range(TA)? What about c= 13 ? Is L7 sector what aboute=p} L7 Ta onto (surjective)?
Describe the solutions of the first system of equations below in parametric vector form. Provide a geometric comparison with the solution set of the second system of equations below. 4x1 +4x2+8X3 = 16 - 12X1 - 12X2 - 24x3 = - 48 - 6x2 - 6x3 = 18 4x7 +4x2+8X3 = 0 - 12X1 - 12X2 - 24x3 = 0 - 6x2 - 6x3 = 0 X1 Describe the solution set, x = X2 of the first system of equations...
3. This example hopes to illustrate why the vector spaces the linear transformation are defined on are critical to the question of invertibility. Let L : → p, be defined by L(p)(t+1)p(t)-plt). (a) Given a basis of your choice, find a matrix representation of I with respect to your chosen basis (b) Show L: P+P is not invertible (e) Let V-span+21-4,+2t-8). It can be shown that L VV. Given an ordered basis for V of your choice, find a matrix...
1 7 -6 13 Given A and b to the right, write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Then solve the system and write the solution as a vector. A= -2 -5 3 b= -8 ܗ - 4 - 6 -2 Write the augmented matrix for the linear system that corresponds to the matrix equation Ax = b. Select the correct choice below and fill in any answer boxes within...
Compute the product using (a) the definition where Ax is the linear combination of the columns of A using the corresponding entries in x as weights, and (b) the row-vector rule for computing Ax. If a product is undefined, explain why. 1 2 - 3 -3 1 1 3 (a) Set up the linear combination of the columns of A using the corresponding entries in x as weights. Select the correct choice below and, if necessary, fill in any answer...
Find g'(x) for the given function. Then find g'(-2), g'(0), and g'(2). g(x) = V7x Find g'(x) for the given function. g'(x) = 0 Find g'(-2). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A g'(-2) = (Type an exact answer.) OB. The derivative does not exist. Find g'(0). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. g'(0) =...
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