It doesn't really make sense to talk about consistency here; it's just a matrix, not a system of equations. We've shown that the row echelon form has $3$ leading $1$'s and thus the matrix …

Feb 22, 2019 · I saw this question somewhere and made me think do 3x4 matrices have an inverse, as I previously that that only square matrices have an inverse. If non-square matrices …

How do you prove that any $3\times4$ matrix has linearly dependent columns? Suppose the columns of your matrix are $\mathbf v_1,\mathbf v_2,\mathbf v_3,\mathbf v_4.$ And suppose …

Apr 16, 2015 · Remember the definition of a matrix to be in reduced row echelon form: The furthest left nonzero entry of each row is a 1 The furthest left nonzero entry of each row has all …

Mar 19, 2015 · The fact that none of the rows in the first matrix is a multiple of another does not mean that the rank of the matrix is $3$. For example, consider the matrix whose rows are $ …

Nov 15, 2021 · I have this matrix below: And i have this question below: Determines whether the row vectors of A are linearly dependent. Explain! Determine the solution quantity for the …

Aug 26, 2012 · 27 I'll illustrate how to understand the LU-decomposition of a particular $3 \times 4$ matrix below. The method works just as well for other sizes since the LU-decomposition …

The Determinant of a Matrix: In mathematics, the determinant of a matrix is a scalar value, meaning that it is a real number that can be found for square matrices. This scalar value can …

Oct 18, 2023 · Find a 3x4 matrix A of rank 2 that contains Span {v1,v2} in its null space. Hint: if a,b,c,d are the entries in the first row of A, what do Av1=0 and Av2=0 tell you about a,b,c,d?

13 To follow up user80's answer, you want to get transformations of the form v --> Av + b, where A is a 3 by 3 matrix (the linear part of transformation) and b is a 3-vector. We can encode this …