Find two 3 x 3 matrices A and B such that det(A + B) + det(A) + det(B) Upload an image or PDF of your hand-written work and

Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

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Q: If A and B are invertible 5x5 matrices, then A+B is also invertible. True False

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Q: Which of the following matrices is not in Row Echelon Form (REF)?

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Q: Find a 2 x 2 orthogonal matrix P whose first row is a multiple of (a) (3,–4), (b) (1,2).

A: Result: Rows (columns) of an orthogonal matrix are an orthonormal basis. Hence, each row (column)…

Q: VýB × VA

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Q: Determine all 2x2 matrices such that A? = I,: A- (: :) 0. b

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Q: Write down the necessary conditions for the matrix B2*2 (2 ∗ 2 matrix) to have an inverse matrix.

A: Necessary conditions for a 2*2 matrix to have an inverse matrix.

Q: Give an example of two matrices A and B such that BA exists, but AB is undefined. Explain why your…

A: Finding the product of two matrices is only possible when the inner dimensions are the same, meaning…

Q: When the inverse of a matrix is multiplied by the original matrix, it produces the: A. matrix of…

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Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

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Q: Let A and B be two skew-symmetric matrices of the same size. Show that AB+BA is symmetric.

A: Given that: Let A and B be two skew-symmetric matrices of the same size. To show: AB+BA is…

Q: Find the range of a (2 × 3) matrix B with rank(B) = 2

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Q: Find a matrix B in reduced row echelon form that is rowequivalent to A, using elementary matrices.

A: Given- 2-40013006 To find- Find a matrix B in reduced row echelon form that is row equivalent to A,…

Q: Let A and B be two square Matrices of the same Size such that A is not invertible (B may or not be…

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Q: Find ∣A−1∣ for the matrix

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Q: Let A and B be matrices such that the product AB is defined. Show that if A has two identical rows,…

A: Let A = [aij] be an m×n matrix and B = [bij] be an n×l matrix. Let C = AB = [cij] be an m×l product…

Q: Find A of the matrix 1- A = 2. -4 2. 1.

A: The inverse of the matrix A of order n is defined as a matrix B of order n such that AB=BA=I, where…

Q: 3. Find all matrices which satisfy the matrix equation (::)(; })-(; :)(::)

A: Here,

Q: What do 2 × 2 matrices represent graphically?

A: 2 × 2 matrices represent:

Q: Find the inverse of the matrix 1 2 3 0 4 5 0 0 6  Using an augmented matrix

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Q: Let A, B and C be 2x2 matrices that are invertible under matrix multiplication. Simplify (A CBC)as…

A: Since you have asked multiple question, we will solve the first question for you.If you want any…

Q: Prove that the product of two n x n anti-diagonal matrices is diagonal.

A: To prove that the product of two n*n anti-diagonal matrices is a diagonal matrix.

Q: Formulate the method for adding partitioned matrices, and verify your method by partitioning the…

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Q: Find nonzero 2 × 2 matrices A and B such that AB = O.

A: Consider

Q: Find two 3 x 3 matrices A and B such that A · B+ B · A Find a 3 x 3 matrix A that is not the zero…

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Q: Find the inverse of the matrix by Gauss-Jordan Elimination (using an adjoined matrix). (If an answer…

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Q: Prove that the product of two upper triangular matrices is always another upper triangular matrix.

A: We have to prove that the product of two upper triangular matrices is always another upper…

Q: Find a family of the matrices that is similar to the matrix

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Q: Write a 4  6 matrix with distinct non-positive entries and find its transpose.

A: The objective is to write a 4×6 matrix with distinct non-positive entries and find its transpose .

Q: Find inverse matrix using Gauss - Jordan Method if available [3 2 -1] A = 6 2 [5 0 1

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Q: Find a 2 x 2 matrix such that 5 1 1 0 2 1

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Q: Let A be an m × n matrix. Explain why the matrix multiplications ATA and AAT are possible.

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Q: Find the inverse of the matrix A using row operation if A is a non-singular matrix, where, 6 -2 -4…

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Q: Using only 0's and l's, find the number n of possible 3 x 3 matrices in row canonical form.

A: We have to make all possible row echelon form ( row canonical matrices ) of 3×3 matrix with 0 and 1…

Q: A matrix which has an inverse is classified as

A: A matrix which has an inverse is classified as                   .

Q: Express the matrix and its inverse as products of elementary matrices. 10-2 A 0 5 4 0 0

A: NOTE: Refresh your page if you can't see any equations. .

Q: Find an LU factorization for the matrix: 1 2 1 2 1 2 -2 0 1

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Q: Find two 2 × 2 matrices such that ∣A∣ + ∣B∣ = ∣A + B∣.

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Q: Create two 2 x 2 matrices A and B, to show that (A+ B)- A +B is not always true. Clearly write A, B,…

A: Give an example of 2 × 2 matrix, in which A + B-1 = A-1 + B-1 is wrong.

Q: Show that it is impossible to find two real 2 x 2 matrices A and B such that AB - BA = dI where d…

A: Take A and B are arbitrary matrices and find AB-BA and analyse the diagonal elements

Q: APPLY A SERIES OF ROW OPERATIONS ONTO THE GIVEN MATRIX "A" TO FIND ITS INVERSE. [ A|1] => [ I|…

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Q: V3 Express 1 as a product of elementary matrices.

A: Solve by matrices

Q: Find a sequence of elementary matrices whose product is the nonsingular matrix below.

A: Given non-singular matrix is :                                                          2-410   To…

Q: Find inverse matrix using Gauss - Jordan Method if available 1 -2 4 A = 8 [-1 -3

A: We have to find the inverse of the given matrix.

Q: Show that there are no 2 X 2 matrices A and B such that AB - BA = I2

A: Given- There are 2×2 matrices A and B. To disprove- That AB-BA=I2

Q: If A, B are two n x n orthogonal matrices, then AB is also an orthogonal matrix. True False

A: Give:  If A , B are two n×n orthogonal matrices. To check: product of matrices A and B are…

Q: Find a sequence of elementary matrices whose product is the given nonsingular matrix.

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Compound Probability

Compound probability can be defined as the probability of the two events which are independent. It can be defined as the multiplication of the probability of two events that are not dependent. 

Tree diagram

Probability theory is a branch of mathematics that deals with the subject of probability. Although there are many different concepts of probability, probability theory expresses the definition mathematically through a series of axioms. Usually, these axioms express probability in terms of a probability space, which assigns a measure with values ranging from 0 to 1 to a set of outcomes known as the sample space. An event is a subset of these outcomes that is described. 

Conditional Probability

By definition, the term probability is expressed as a part of mathematics where the chance of an event that may either occur or not is evaluated and expressed in numerical terms. The range of the value within which probability can be expressed is between 0 and 1. The higher the chance of an event occurring, the closer is its value to be 1. If the probability of an event is 1, it means that the event will happen under all considered circumstances. Similarly, if the probability is exactly 0, then no matter the situation, the event will never occur.