a) Let A be a 2 × 2 matrix. Show that for ALL choices of scalars a, that if A = aI2, then AB = BA for ALL 2 × 2 matrices B.   b) For ALL 2×2 matrices A where A is NOT a scalar multiple of I2, find a 2 × 2 matrix C with AC ̸= CA (Hint: use matrices with a single nonzero entry.)

Q: Let A and B be n x n invertible matrices. Use matrix algebra to simplify A(A¯¹ + B¯¹)B.

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Q: Part A) Compute the matrix-vector product Ax using the row-vector rule. Part B) Write the…

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Q: b) Consider the following matrices: Solution: M₁ = [1 −7], M₂ = [1 2], M₁ = (1 1]. A = [23], B= [13…

A: Step 1: Determine if A is in the set Span({M1​,M2​,M3​}).Step 2: Determine if B is in the set…

Q: Find two non zero matrices A and B such that AB = 0. %3|

A: Find the two matrix which satisfy the given condition

Q: Let A = 2 2 5 2 4 (a) Use elementary row operations to find the inverse of A. (b) Use the elementary…

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Q: Use row operations to change the matrix to reduced form. 1 1 1 18 5 6 7 24 1 1 1 18 5 6 7 24

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Q: Suppose A is a 3x3 matrix. Let B be the matrix obtained from A by performing the following…

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Q: How can we determine the cofactor for each element in a matrix?

A: Query- How can we determine the cofactor for each element in a matrix? Answer-  The first step…

Q: Give an example example of a 3x5 matrix in BREF where RX=0 has unique solution.

A: The aim is to find an example of  matrix in RREF where  has a unique solution.

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.