Homework Answers
A scalar matrix is simply a matrix of the form XI, where I is the nxn...
A scalar matrix is simply a matrix of the form XI, where I is the nxn identity matrix. (a) Prove that if A is similar 1 to \I, then in fact A= \I. (b) Show that a diagonalizable matrix having only one eigenvalue is a scalar matrix. 1 100 100 (c) Prove that o 100 is not diagonalizable. 0 0 1 1
1. Write a MATLAB function that takes a matrix, a row number and a scalar as...
1. Write a MATLAB function that takes a matrix, a row number and
a scalar as
arguments and multiplies each element of the row of the matrix by
the scalar returning the
updated matrix.
2. Write a MATLAB function that takes a matrix, two row numbers and
a scalar as
arguments and returns a matrix with a linear combination of the
rows. For example, if the rows
passed to the function were i and j and the scalar was m,...
Sean A y B eventos tal que P(A o B) = 0.76, P(A) = 0.65 y...
Sean A y B eventos tal que P(A o B) = 0.76, P(A) = 0.65 y P(A y B) = 0.20 a) P(B) b) P(ANB) c) P(Äy B) 0.65 Check Las probabilidades de tres eventos A. By C se distribuyen en el siguiente diagrama de Venn. B с 0.25 0.02 0.2 0.05 0.1 0.15 0.21 А 1. P(A) = 0.51 2. P(ANC) = 3. P(BUC) = 4. P(B) = 5. PLĀNBOC) =
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set o...
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
5. For the following state space systems, determine the controllability matrix and the observability matrix O....
5. For the following state space systems, determine the controllability matrix and the observability matrix O. State whether they are controllable and/or observable based on the matrices. a) * = 12 *_]x+[{]u; y = [1 2]> b) *="2)+ [a] u y = [1 0x 1-1 0 c) i = 0 -2 lo 0 y = [1 0 2]x 0 1 11] 0 x + 1 u -3 10)
1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equati...
1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equation and initial conditions.
1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equation and initial conditions.
1. Why the following sets are not vector space? with the regular vector addition and scalar...
1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. a) V = {E: * > 0, y 20 with the regula b) V = {l*: *y 2 o} with the regular vector addition and scalar multiplication. c) V = {]: x2+y's 1} with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t + t2 is a basis for P, the set of all polynomials with degree less...
linear algebra 1. Determine whether the given set, along with the specified operations of addition and scalar multiplica...
linear algebra
1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
/** * multiply a scalar value (constant) into a matrix. * IMPORTANT: the matrix passed should...
/** * multiply a scalar value (constant) into a matrix. * IMPORTANT: the matrix passed should NOT be modified. * @param m: matrix from which scalar is to be subtracted * @param b: scalar to be subtracted * @return resulting Matrix */ public static Matrix multiply(Matrix m, double b) { Matrix result = new Matrix(); return result; //to be completed } /** * add to matrices. * IMPORTANT: neither of the passed matrices should be modified * @param m: matrix...
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size...
1) a) If A is a 4×5 matrix and B is a 5×2 matrix, then size of AB is: b) If C is a 3×4 matrix and size of DC is 2×4 matrix , then size of D is: c) True or False: If A and B are both 3 × 3 then AB = BA d) The 2 × 2 identity matrix is: I = e) Shade the region 3x + 2y > 6. f) Write the augmented matrix...
A scalar matrix is simply a matrix of the form XI, where I is the nxn identity matrix. (a) Prove that if A is similar 1 to \I, then in fact A= \I. (b) Show that a diagonalizable matrix having only one eigenvalue is a scalar matrix. 1 100 100 (c) Prove that o 100 is not diagonalizable. 0 0 1 1
1. Write a MATLAB function that takes a matrix, a row number and
a scalar as
arguments and multiplies each element of the row of the matrix by
the scalar returning the
updated matrix.
2. Write a MATLAB function that takes a matrix, two row numbers and
a scalar as
arguments and returns a matrix with a linear combination of the
rows. For example, if the rows
passed to the function were i and j and the scalar was m,...
Sean A y B eventos tal que P(A o B) = 0.76, P(A) = 0.65 y P(A y B) = 0.20 a) P(B) b) P(ANB) c) P(Äy B) 0.65 Check Las probabilidades de tres eventos A. By C se distribuyen en el siguiente diagrama de Venn. B с 0.25 0.02 0.2 0.05 0.1 0.15 0.21 А 1. P(A) = 0.51 2. P(ANC) = 3. P(BUC) = 4. P(B) = 5. PLĀNBOC) =
IT a) If one row in an echelon form for an augmented matrix is [o 0 5 o 0 b) A vector bis a linear combination of the columns of a matrix A if and only if the c) The solution set of Ai-b is the set of all vectors of the formu +vh d) The columns of a matrix A are linearly independent if the equation A 0has If A and Bare invertible nxn matrices then A- B-'is the...
5. For the following state space systems, determine the controllability matrix and the observability matrix O. State whether they are controllable and/or observable based on the matrices. a) * = 12 *_]x+[{]u; y = [1 2]> b) *="2)+ [a] u y = [1 0x 1-1 0 c) i = 0 -2 lo 0 y = [1 0 2]x 0 1 11] 0 x + 1 u -3 10)
1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equation and initial conditions.
1. (a) If y )Fx), and y satisfies the initial conditions y(O)o and y(O) o, show that [Notice that yc)F) and use (10),) (b) Verify that this expression satisfies the prescribed differential equation and initial conditions.
1. Why the following sets are not vector space? with the regular vector addition and scalar multiplication. a) V = {E: * > 0, y 20 with the regula b) V = {l*: *y 2 o} with the regular vector addition and scalar multiplication. c) V = {]: x2+y's 1} with the regular vector addition and scalar multiplication. 2. The set B = {1,1+t, t + t2 is a basis for P, the set of all polynomials with degree less...
linear algebra
1. Determine whether the given set, along with the specified operations of addition and scalar multiplication, is a vector space (over R). If it is not, list all of the axioms that fail to hold. a The set of all vectors in R2 of the form , with the usual vector addition and scalar multiplication b) R2 with the usual scalar multiplication but addition defined by 31+21 y1 y2 c) The set of all positive real numbers, with...
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