Linear Algebra | Senioritis

John Rhodes
June 21, 2023
Linear Algebra

Proving Linear Dependency: The Relationship Between Z And Span{X, Y}.

HW 4: If {x, y} is linearly independent, and if z is in Span{x, y}, then {x, y, z} is linearly dependent. TRUE. Since z is in...

John Rhodes
June 21, 2023
Linear Algebra

Proving The Statement: If A System Has Infinitely Many Solutions, The Matrix Isn’T Invertible.

HW 5: Let A be an n × n matrix, and b be a vector in R^n . If the system Ax = b has infinitely many...

John Rhodes
June 21, 2023
Linear Algebra

How To Prove That If Ab = Ac And A Is An Invertible Square Matrix, B = C

HW 5: Let A be an invertible square matrix. If AB = AC, then B = C. TRUE. AB = AC–> A^−1 (AB) = A^−1 (AC) –>...

John Rhodes
June 21, 2023
Linear Algebra

Matrix Multiplication: Debunking The False Claim That Ab = [A1B1 A2B2] For 2 X 2 Matrices A And B.

If A and B are 2 x 2 with columns a1, a2 and b1, b2, respectively, then AB = [a1b1 a2b2]. False because it violates the definition...

John Rhodes
June 21, 2023
Linear Algebra

The True Statement About Matrix Multiplication: Columns Of Ab As Linear Combinations Of Columns Of B Using Weights From Corresponding Columns Of A.

Each column of AB is a linear combination of the columns of B using weights from the corresponding column of A. False because the roles of A...

John Rhodes
June 21, 2023
Linear Algebra

Mastering Matrix Mathematics: The Distributive Property Of Matrix Multiplication Over Addition.

AB + AC = A(B + C) True because this is the distributive property for matrices A, B, and C also mentioned in Theorem 2B. The statement...

John Rhodes
June 21, 2023
Linear Algebra

Matrix Transpose: Proving A^T + B^T = (A + B)^T.

A^T + B^T = (A + B)^T True. See properties of transposition. Also should be able to think through to show this. When we add corresponding entries,...

John Rhodes
June 21, 2023
Linear Algebra

The Transpose Of A Product Rule For Matrices

The transpose of a product of matrices equals the product of their transposes in the same order. False because it should be reverse order not same order....

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