(a) Determine if the transformation defined by each of the following standard matrices is injective and/or surjective. i. 1 0 1 1 3 0 2 NLON 4 -2 14 3 11 6 ii. 1 0 -1 221 -4 1 −1 -3 20 -1 -5 0 -1 -3 iii. iv. -2 1520 -4 троф 403 0 0 -2 1 3 1 -2 3 0 -5 1 -2 4 0 -5 -2 4 -4 -4 -1 (b) Which of the above transformations was bijective?

Q: Determine if the specified linear transformation is (a) one-to-one and (b) onto. Justify each…

A:

Q: Q2] a) Write each (PRODUCT) of the following as a single matrix: i -17 2 -2 -1]-i -2 5] -2| -1 1 -1]…

A:

Q: Which of the following matrices is equal to 2 1 -1 3 ³ [²₂²] + ² [¯ 2² _ ;]³² ? 03 -7 4 1 1 2 -4 4 4…

A:

Q: x- y+10z = 29 x+ y+2=6

A:

Q: Let T,(x1,x2) = (+4x1 – 5z2, +1æ1 – lz2), and T2(x1,X2) = (- 321 – 5æ2 , +5æı + 8x2). Write the…

A: To find the standard matrices for T1,T2 and T10T2.

Q: Compute AB, det(A), det(B), det(AB), and det(A + B) for the following matrices. 1 0 -1 4 0 5 0 1 A =…

A: Given that :- A=50113-1101 , B=10-1401010 find AB,detA,detB,detAB,detA+B

Q: Find the QR factorizations of the given matrices: [211 a. A =

A: So, Answering question a.

Q: 2-3 Find AB for each of the following metrices:- -lo DA•[ -21, 8-[] L 3 2) A= 3 4. 2 -33 5 13 1J

A:

Q: find A*B and B*A for the matrices A= 10 1 2 1 1 3 2 -1 B= 0 0 3 1 2 4 -1 -1 0

A: We have to find AB and BA for the matrices                                             A=10121132-1…

Q: Write B as a linear combination of the other matrices, if possible. (If not, enter DNE in all…

A:

Q: (a) Find the standard matrix for the standard matrix defined by the following transformations: wi =…

A:

Q: A= [2002], Now imagine you have a square (0,0), (1,0), (0,1) and (1,1). To what geometric object the…

A:

Q: Q14: Create a model using appropriate block to concatenate vertically the matrices A, B, and C…

A:

Q: Consider the following matrices: -(; ) -) -() 0. 1. -1 3 A В 1 -3 C = |3 4 2 1 2 2 -1 Perform each…

A: a A+B is not define because size of matrix A and B is not same  A is 2*2 and B is 3*2 matrix so...…

Q: Find the inverse of the given matrix using Adjoint Matrix: 1 -1 0 0 -1 2 -1 0 0 -1 2 -1 0 0 -1 2

A: We know A-λI = 0 A-λI =    1-1   0   0-1   2-1   0  0-1   2-1  0  0-1   2-λ1000010000100001 = 0

Q: iagonalize the following matrix: 21 4 1-4 31 -1 24001₁ 111-12 C - 0

A: A matrix is diagonalizable if A.m. of each eigen value = g.m. of corresponding eigen value

Q: 1. Multiply the following matrices; if you can't multiply the matrices, then explain why. 2 -3 1 1 3…

A: This question is related to matrix multiplication, we will solve it using given information.

Q: Express A as a product of elementary matrices where 3 A = [2²4] 1 And express each elementary matrix…

A: Let us find the elementary matrices.

Q: <= [-5 1 is the product X = E₁ E₂E3 of elementary matrices E₁, E2, E3, find -5 35 E₁ = If x= 03-894…

A:

Q: Diagonalize the following matrix: 1 13 5 7 -5 -7 -1 -1 7 90 06 0 00-12 060 − 1 1 − 1| -1 0 1 1 10 1…

A: Given matrix 11357-5-7-1-17

Q: Exercises A. Consider the matrices below: 07 [1 C = 2 [1 A = 2 -11 2 B = 3 -1 7 5 11 5 3 [12 E = |2…

A:

Q: 4- Determine the rank of the following matrices: 2 8] [3 4 5 [1 7 6 ii- A=1 2 3 5 3] [3 9 21 iii- A…

A:

Q: 2a + 56+c —а — 36 — 2с 3a + 76 +c -4a – 96 –c 2. T(а + bx + сх*). |

A: The objective is to write down the matrix of the given linear transformation withrespect to the…

Q: Find the rank of the following matrices: 1 2 2 3 3 2 1 тank(A)— 2 3 таnk(A)—

A: We use the definition of the rank of a matrix to find the rank of given matrices.

Q: Find the B-matrix for the transformation x-Ax when B=(b₁,b₂, b3}. A= -7 -72 1 17 -4 -72-21 The…

A: Solution :-

Q: Suppose that vertices of a hut-shaped triangle on a computer screen are given by the coordinates (1,…

A:

Q: 9. Find the inverse of the matrix 0 0 k₁ 0 0 k, 0 3 0 0 k₁ 0 0 k₂ 0 0

A:

Q: evaluate the matrix

A:

Q: Q5: Write the following as a product of elementary matrices. 8 00 1 1 -2 (а) |0 -3 1 0] 0 2 0 5 0 20…

A:

Q: Which of the following 3 x 3 matrices are in row-echelon form? Note: Mark all of your c 1 -7 -8 1 1…

A: The matrix is said to be in row echelon form if: The first non-zero element in each row, called the…

Q: Diagonalize the following matrix: 21 0 4 - 1 -4 3 1 - 1 400 0 1 0 00-2 not diagonalization 40 0 02 0…

A:

Q: Q4. (A)_ If a-12 4 68 10; 31415; 24 6 8 10; 1 234 5; 4790 61. find the sub matrices with explain it.…

A: Remark:  Let a be an m*n matrix, then a(:, p) gives  sub-matrix of order m*1 with elements of p-th…

Q: Use the inverse matrices to find (AB)¯¹, (A7)¯¹, and (24)¯¹. 1 1 1 2 2 1 3 1 244 A-1 = (a) -2 1 3 2…

A:

Q: Derive the matrix that performs the following consecutive transformations (in augmented form): 1-…

A: (1) Let T be a transformation that translate 2- unit along x-axis. Therefore: Txyz=x+2yz Therefore…