The given T is a linear transformation from R² into R². Show that T is invertible and find a formula for T1. T(x₁,x₂) = (4x₁ - 5x2, − 4x₁ + 1 -7x₂) To show that T is invertible, calculate the determinant of the standard matrix for T. The determinant of the standard matrix is (Simplify your answer.)

Q: Let A 1 1 A = 1A -1 1 Then answer the following. (a) Determine a;ı · (a2 x a3), for i = 1, 2, 3. (b)…

A:

Q: [ab]. C d 6) (i) Compute the adjoint of A= (ii) Show that the determinant of A equals the…

A:

Q: Without expanding along any row or column, use the properties of determinants to find the…

A:

Q: Consider the system shown here. Describe the pattern associated with constructing the determinants…

A:

Q: Find the determinant of the matrix A = [w v], where v and w are as shown below and the area of the…

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Given T(x1,x2)=(6x1-5x2,-6x1+8x2) So T(1,0)=(6,-6)T(0,1)=(-5,8) So the standard matrix for T is…

Q: 21 -15 24 30 A = -10 24 -32 18 -40 22 32 -35

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Here, the given T is a linear transformation from ℝ2 into ℝ2. It has to be determined T is…

Q: Given the following matrix, find (1) the determinant and (2) the multiplicative inverse of the…

A: The determinant and the multiplicative inverse of the determinant for the given matrix are provided…

Q: Consider a 20x20 invertible matrix A whose determinant is 2. Let B be the matrix obtained from A by…

A: Given: A is a 20×20 matrix. The determinant of matrix A is 2. B is the matrix obtained by…

Q: Use Gaussian elimination to determine the determinant of the matrix: 1 1 1 1 1 1 44 M = 1 -1 2 -2 -1…

A: To determine the determinant of the matrix  M  using Gaussian elimination, we need to perform row…

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A:

Q: Show your complete solutions: 1. Using cramer's rule: 2 x1-3 x2 +1.4 x3= -5.2, 1.3 x1 + x2+2.4 x3=…

A:

Q: The given T is a linear transformation from R2 into R². Show that T is invertible and find a formula…

A:

Q: So  I will give you a matrix. For that matrix find the determinant and show  that the matrix is…

A: The given matrix is .We need to find the determinant and identify whether it is invertible or not.If…

Q: Find the determinants

A:

Q: . Solve these two simultaneous linear equations using Cramer's method of determinants.

A: Given,

Q: Which of the following is the determinant of the 2 x 2 matrixA= (A) ad-be (B) be- ad (C) (D) ad-bc

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A: Introduction: The linear transformation is invertible if and only if the corresponding matrix is…

Q: Describe the determinants D, Dx, and D, in terms of the coefficients and constants in a system of…

A: Consider the system of two equations in two variables as follows: a1x+b1y=c1a2x+b2y=c2 By using…

Q: Evaluate the determinant A by any method, |1 3 6 2 1 0 2 |0 A = |3 2 3 0 2 9 5 1 0 10 0 8 6 0 1 2

A: Consider , A = 1310206223302951010086012 We need to find determinant of A. For that we will use ,…

Q: Let A be a matrix given by: ATTACHED IN IMAGE Find determinant of matrix A. For which values of a…

A: Step 1: Step 2: Step 3: Step 4:

Q: Alsan tet A = and B = 15 [4 101 l7 15J 3 (a) [ Let c 3. Find cA. (b) ts] Find A + B (c) Find the |A|…

A: use property of matrix.

Q: Let i=√√-1, Find the determinant for the matrix 2 3-i 4-i 3+1 -2 2+i in the form a + ib and find the…

A:

Q: Show that the determinant of the matrix B = xl – A, where I is an identity matrix and A = [1 2 01…

A:

Q: The given T is a linear transformation from R² into R². Show that T is invertible and find a formula…

A:

Q: [1 2 -1] 1. If A = 3 2 4, verify that detA = detA". L1 3

A:

Q: a (a) Find the value of a for which 1 and 4 are perpendicular. -0-0 1 0 -1 (b) If A 0 22 , calculate…

A:

Q: The given T is a linear transformation from R2 into R² Show that T is invertible and find a formula…

A:

Q: Consider matrix A E R33, such that det(A) = 3. Find determinant of matrix B = A-1. (2 · I) · A4.

A: