Let 0 3 0 1 1 2 2 1 A = -1 B : 0 1 1 2 0 1 -2 Compute det(AB), det(A-'B-!) and det(2A) where 2A means each entry in A is multiplies by 2.

Q: 1 Consider the system Ax = b where A = -3 -2 and b -2 .A {[} basis for the null space of A is given…

A: Solution to the system

Q: [2 8) Use the Gauss-Jordan method to find the inverse of the matrix A: %3D

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Q: Show that in the simplex method if a variable x, leaves the basis, it cannot enter the basis in the…

A: Solution ) the simplex method is mainly focused on minimizing  the function   Let us suppose we take…

Q: Show that there is no matrix A E M250x250 with real entries satisfying AAT = -I.

A: Given that A is real ( All entries are real)  square matrix of order 250×250. The trace of any real…

Q: Suppose A is the 3 x 3 zero matrix (with all zero entries). Describe the solution set of the…

A: To prove  Ax = 0

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Q: Select all of the elementary matrices belo 1 0 1 0 1 0 0 0 1 0 0 1 0 1 0 1 0 0 -1 -1 -1 0 01 1 0 1

A: Answer: -1000-1000-1

Q: 2.3 Compute the principal square root of each of the llowing positive semidefinite matrices. (b) 2 3…

A: Please find the solution in next step

Q: 4. Give an example of an indefinite quadratic form on R³ whose corresponding symmetric matrix has no…

A: Let Q(x1,x2,x3)=-x12-2x1x2+6x1x2+3x22-2x2x3-x32 be a quadratic form whose symmetric matrix is…

Q: z= 5x, + 12x2 + 4 x, S.t X, + 2x2 + X, s 8 2 x, - X2 + Xạ = 8 where x,, X2, Xs 20

A: For a Minimization Problem, The constraints must be in the form≥ in the standard Primal Form.…

Q: (b) Show that the residuals of the least squares solution of a system of overdetermined equations Ax…

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Q: Suppose that you are on the bottom left corner (green) of a 9 x 12 grid of city blocks. (a) to the…

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Q: Show that the zero matrix is the only 3 × 3 matrix whose null space has dimension 3.

A: Given- A zero matrix of 3×3 order. To show- that the zero matrix is the only 3 × 3 matrix whose null…

Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

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Q: Let C be a 5 x 7 matrix with a rank 4. (1) What is the dimension of the solution space of Ax 0?

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Q: Construct 3 × 2 matrices A and B such that Ax = 0 has only the trivial solution and Bx = 0 has a…

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Q: 3. 3 If A is non singular matrix whose mverse 2. Al = fad A.

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Q: Let A be 7×9 matrix. Knowing that Rank (A) 3. Then Nullity(A) is equal to: ||

A: Rank nullity theorem Let T:V→W  be a linear transformation on finite dimensional vector spaces over…

Q: Enter the missing coefficients for the row operations. 1 0 (1) O R, - R;: 0 3 1 15 5 2 -4 28 1 0 O…

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Q: Find a 3 × 1 matrix x with entries not all zero such that

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Q: 5. Verify that the product of the non-singular matrix and its inverse from the previous problem is…

A: (5) Given matrix A=32−22 and its inverse is A−1=1102−223. We have to verify that AA−1=I2…

Q: Show that A 2 = 0 is possible but AT A = 0 is not possible (unless A = zero matrix.

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Q: Suppose that collA) = IR+ 4x7 matrix A has 4 lead terms Then and NCA) = R³ %3D %3D

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Q: 2 -3" A = 2 –1 4 4 3 -2

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Q: Find a 3 x 1 matrix x with entries not all zero such that 1 2 -1 Ax = 1x, where A 1 1 -4

A: A=1  2-11  0  14-4  5 Now let x=abc be the required matrix. Now consider, Ax=1x⇒1  2-11  0  14-4…

Q: 1. Show that six (or more) lines that have a common line of intersection (a common transversal) are…

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Q: Findthe Linear Eransfromation whose matrix MT with regard to the base to mec2And the natural ruleto…

A: Given T:C2→C3 be a linear transformation whose corresponding matrix is given  MT=i-i1+i-21-1+2i and…

Q: Show that the first least squares assumption, E(ui | Xi) = 0, implies thatE(Yi | Xi) = β0 + β1Xi.

A: Consider the regression equation is Yi = β0 + β1Xi + ui for all I = 1,2,….,n, where Yi is the…

Q: 2) Show that the three columns on the left all lie in the same plane: 0-0-0-0 If the right hand side…

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Q: If (A2, Ag) is optimal basis for Max z = 2x, + 4x,+ 4x3 - 3x4 s.t. X, + X2 + X3 = 4 X, + 4x, + X4 =…

A: Note:- We can solve it using two ways. Either we can solve it, by converting it in dual then solve…

Q: How many rows and columns must a matrix have in order to define a mapping from R5 into R7 by the…

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Q: Ч. W is the set of all 2x2 upper triangular matrices in Mzx2 (IR).

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Q: Show that the matrix A = singular. 1 -2 3 4 0 5 0 is 60

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Q: 2 3 Show that the matrix A is singular. 4 6

A: Concept used: Singular matrix are the matrix that is not invertible. In other words the determinant…

Q: (c) 0 is neither diagonalizable nor

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Q: Suppose a 3x8 matrix has a rank 3, then the dimension of the Null space. Dimension of the Row space…

A: Ans: Given a 3×8 matrix has a rank 3. We want to find the dimension of the null space, dimension of…

Q: Show that matrix multiplication is associative i.e. A(BC) = (AB)C when- ever the multiplication is…

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Q: Го 6. Show that the matrix does not have an LU decomposition by considering the product [l11 0 [121…

A: Given :0110

Q: Find the null space of matrix A which is 1 3 13] 7 3 8 A =-2 -5 -3 0 3 2 6. 24 3 13 1 2. 6 3.

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Q: 6. To identify 3 x 3 matrix Abr fis positive definite if and only if cfr r> 0, r²- ab >0 and 4>0. O…

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Q: / Find a Row A, CoL A, Null (A), whore. A= bazis and dimension Lor 2. 1- -31 -2

A: we have to solve given problem:

Q: () The operation of subtraction A, BHA-B of matrices A, Bhaving the same size is defined by as…

A: Given: (i) S and T are relations on a finite set A, MS and MT are matrices of S and T respectively.…

Q: 4. Prove: If A and B are both n x n matrices, then det(AB)= detAdetB. (Only use 2x2 matrices)

A: Given A and B  n×n  matrices to prove  det(AB)=det A det B

Q: [2 3 find the invers of matrix A by using the elementary row operation, where A = 5.

A: For finding the inverse of any matrix A, at first we augment it with an identity matrix on the…

Q: Find the null space of matrix A which is 1 1 3 7 6 3 8 A = -2 -5 -3 0 3 0 2 4 3 5 13 1 3. 3. 2.

A: A null space of matrix A is the space that consists of all the vectors X such that AX=O…

Q: 3. The following row operations were applied in order to a 3x3 matrix A to get matrix 2B. Compute…

A: This is a problem of linear transformation.

Q: (i) Compute each Ax by dot products of the rows with the column vector: [i 1 1] (a) 2 1 1 3 2 1 -5 1…

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Q: nd the inverse of the matrix 1 0 -2 1 4 -3 4 oices: 8. -3 1 8 3 1 а. 10 4 1 C. 10 4 1 -7/2 3/2 1/2…

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Q: Solve the following system using the Gaussian algorithm: 2x1 – x2 + 3x3 = 0 -2x1 + x2 - X3 = -2 x -…

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Q: For matrices M and N, the 3rd column of NM is all zeros. Matrix M has 5 columns and none of them are…

A: Please find the detailed solution in next steps

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.