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D H said:You don't need the determinant to solve this problem. You are just looking for some a, b such that [itex]a\,\mathbf v_1 + b\,\mathbf v_2 = \mathbf v_3[/itex] -- or show that no such a, b exist.
Nope. Edit: Oops, my bad. I checked it again after seeing DH's post, and I'm the one who messed up.judahs_lion said:Thanks so a = -7, b =1;
Good. So what does that mean in terms of the problem? (You need to determine whether v1, v2, v3 are dependent or independent.)judahs_lion said:Thanks so a = -7, b =1;
That looks good.Span(v1,v2,v3) = {<a, -a; c , 0> : a, c belong to R} ?
D H said:Good. So what does that mean in terms of the problem? (You need to determine whether v1, v2, v3 are dependent or independent.)
That looks good.
D H said:Correct.
No, a matrix cannot be a vector. A matrix is a rectangular array of numbers or symbols, while a vector is a mathematical object that has magnitude and direction. While they may look similar, they serve different purposes and cannot be used interchangeably.
A matrix is a 2-dimensional array of numbers or symbols, while a vector is a 1-dimensional object that has magnitude and direction. Matrices are used for operations such as addition, subtraction, and multiplication, while vectors are used for representing physical quantities such as force and velocity.
No, a matrix is not a type of vector. They are two distinct mathematical objects that have different properties and uses. While they may share some similarities, they cannot be used interchangeably.
Yes, a vector can be represented as a matrix in some cases. For example, a column vector with n elements can be represented as an n x 1 matrix, and a row vector with n elements can be represented as a 1 x n matrix. However, this does not change the fact that they are different mathematical objects with different properties.
No, a matrix and a vector cannot be multiplied together. In order for two matrices to be multiplied, the number of columns in the first matrix must be equal to the number of rows in the second matrix. Since a vector only has one row or column, it cannot satisfy this requirement for matrix multiplication.