a12 a11 is the matrix: a22 a21 (4) The adjugate of a 2 x 2 matrix A a12 a22 adj(A) a11 a21 (a) Show that adj (A) A A adj (A) det(A)I2. (b) Show that det(adj(A)) det(A)

Q: 0-1 *b. Construct a matrix whose column space contains1 and 1 and whose nullspace contains and or…

A: THE REQUIRED MATRIX IS A

Q: 2 1 -1 3 1 2 1 2 0 b) Calculate the rank of the matrix P = 3 1 1 1 |-1 -5 -3 -7 3

A: Given,

Q: Determine if the matrix is nonsingular. Explain. [1 3 21 1 4 l1 -7 21

A:

Q: |3 1 2 - Transpose of the Matrix 2 -1 2 |-1 2 3 1 2 -1 -2 2 -1 a. C. -2 -1 3 -2 3. 2. 1 -1 -1 -2 0…

A:

Q: Determine the diagonal matrix. 1 -3 -2 0 0 0 4 (1 3 5)

A:

Q: 0 1 2 3 0 0 1 2 A = 0 0 0 1 12 - 0 0 0 0 A=[a] matrix can be expressed as

A:

Q: True or false? det(A) is a number, not a matrix.

A:

Q: 3 Evaluate Inverse Matrix A-¹ = −1 2 1 2 2-1 1 1

A: The given matrix A-1=312-12-1211 we have to find the inverse matrix of A-1. Inverse of an matrix:…

Q: A is invertible. Is it possible for A³ to be an identity matrix without A being invertible? Explain.…

A:

Q: Orthogonally diagonalizable the following matrix -4 -2) A = -4 5 2 -2 2 2

A:

Q: 24 --8 Find the rank of the matrix A =0 1 -2 4 8 -18 rank(A) =

A: given matrix is  A=-24-801-2-48-18 to find the rank of matrix

Q: Matrix Given A=  3 −1                 −3 1 compute 4A

A: Given that  Matrix A  To find the 4A

Q: Construct a 2 X 2 symmetric matrix A with A [2] = -9 and A a12 If A = a21 a22 then the value of a11…

A:

Q: State the dimension of the matrix.   −3 3 7 0   0 1 14 6

A: Given that, the matrix is          -337001146 Here, the number of rows are 2.   &  the number of…

Q: Find a two-by-two matrix such that: -9 5 1 0 3 5 0 1

A:

Q: Diagonalize the matrix 1 0 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix D…

A:

Q: -2 -1 -3 1 Determine the rank of the matrix 1 0 1 -1

A: Rank of the matrix

Q: a) ir(A - 1)1- ( -2) %3D Find the matrix A

A:

Q: 1 -2 Diagonalize the matrix B 3 -4 ||

A:

Q: 6. Let A be a 2x 2 matrix such that (a) The above equations can be written in the form A -1 0 -1 0 B…

A: The objective is to find the matrix B. heck whether the matrix B is diagonalizable or not and also…

Q: Diagonalize the matrix 1 0 -1 A = -2 3 -1 -2 0 2 In other words, you need to find a diagonal matrix…

A:

Q: A. Construct a 2 × 2 matrix that is invertible but not diagonalizable. Also provide the inverse of…

A:

Q: True or false: Two columns of a matrix may be interchanged to form an equivalent matrix.

A: Known fact: Any elementary row transformation of matrix produces an equivalent matrix.

Q: Give an example showing that the rank of the product of two matrices can be less than the rank of…

A:

Q: Give an example of a 3 × 3 matrix with real inputs that is not similar to a matrix diagonal

A: A matrix is said to be a diagonalisable  if it is similar to a diagonal matrix. Therefore we need to…

Q: Construct an example of an 4×3 matrix with rank 1: You can resize a matrix (when appropriate) by…

A: Rank of Matrix: A n×m matrix has rank k , if k is the  maximum  number of its linearly independent…

Q: (A" – 21) * - | ) 3. Determine the matrix A if

A:

Q: 2.x1 + 3x2 + x3 – 11x4+ 4x5 = 30 5x, – 2x2 + 5x'3 – 4x4 + x5 = 36 T1 – x2 + 3x3 - 3x4 + 5x5 == 23 -…

A:

Q: 3. (30 points) Diagonalize the matrix A = 5 0 1 -1 05 0 0 0 0 4-3 0 -2 0-3 if possible.

A: 5000050000-30000-3

Q: Finding the matrix ofS0T (a) by direct substitution and (b) by matrix multiplication of [S] [T].

A: Finding the matrix of S∘T (a) by direct substitution  Given  Tx1x2 = x1+2x2-3x1+x2Sy1y2 =…

Q: 2, 1 0 2 0 0 0 2 0 0 0 2 Are the matrices 2 1 and similar? Yes No 0 2

A: Given matrices are  210021002 and 200020002

Q: 4] -9 0 -8 1 1 -2 -2 13 Consider the matrix -4 3 -1 2 1

A: let B=1-2-21342-43-90-121-81 claim- to find the right inverse of the matrix

Q: Identify the elementary row operation(s) being performed to obtain the new row-equivalent matrix.

A:

Q: Linear algebra

A:

Q: 1 1 -1)|X1 5 5 2 10 X2 20 3 2 5 X3 14 II

A: Introduction: A diagonally dominant matrix is a square matrix such that in each row, the absolute…

Q: An A12 [ A21 A22. A22 = [-7 7]. Fill in the block matrix. -9 -5 where A11 A12 9 , A21 = [3], and -4…

A:

Q: 1. What is the Matrix 2. What is the order of Matrix 3. What is the type of Matrices 4. What is the…

A:

Q: Find a square root of the matrix 13 0 18 A = -5 0 -6 - -6 -8 In other words, find a matrix B such…

A:

Q: 2. Diagonalize the matrix: 1 0 -2 1 1 1 -1

A:

Q: Express the matrix 1 0 A = and its inverse as a product of two elementary matrices. The matrix A can…

A:

Q: Orthogonally diagonalize the matrix 1 -1 -2 A -1 2 -2 3

A: Given:   A = 1-1-2 -120 -203

Q: Construct an example of an 3x5 matrix with rank 2: You can resize a matrix (when appropriate) by…

A:

Q: Let a - .- 3 -1 21 A = [ 1.8 = ; -21 -31

A: The Addition or Subtraction of matrices is possible only when matrices are of same order.

Q: 3 Evaluate Inverse Matrix A-¹ = -1 2 12 2 1 -1 1

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.