Suppose A is a 5×7 matrix. How many pivot columns must A have if its columns span R5? Why? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The matrix must have pivot columns. If A had fewer pivot columns, then the equation Ax = 0 would have only the trivial solution. O B. The matrix must have pivot columns. Otherwise, the equation Ax = 0 would have a free variable, in which case the columns of A would not span R. O C. The matrix must have pivot columns. The statements "A has a pivot position in every row" and "the columns of A span R5" are logically equivalent. O D. The columns of a 5x7 matrix cannot span R5 because having more columns than rows makes the columns of the matrix dependent.

Q: 4. Solve the system below using matrices and matrix operations. Write the final answers in exact…

A:

Q: Let A be a 4×5 matrix with 4 pivots. Do the columns of A span R4? Do they span R5? Justify your…

A: As A is a 4 x 5 matrix with 4 pivots so, it has a pivot in its every row. So, yes the columns of A…

Q: Let A = {ª₁,2,ª3} and B = a₁ =3b₁ b₂, a₂ = − b₁ + 5b₂ + b3, a3 = b₂ − 2b3. a. Find the…

A: a. Find the change-of-coordinates matrix from A to B.b. Find [x]b for x = 2a₁ +3a2+ a3.

Q: Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly…

A: Given that, A is a 7 x 5 matrix.Now, how many pivot columns must A have if its columns are linearly…

Q: Use the given inverse of the coefficient matrix to solve the following system. 7x, +3x2 = 6 %3D A 1…

A:

Q: Suppose A is a 7x5 matrix. How many pivot columns must A have if its columns are linearly…

A: If A is m×n matrix with m>n then number of pivot columns is equal to number of linearly…

Q: A man has twenty coins consisting of dimes and quarters. If the dimes were quarters and the quarters…

A: Given: A man has twenty coins consisting of dimes and quarters. If the dimes were the quarters and…

Q: (x-3y +3z = -8 7x+y +2z = 6 3x +2y - z = 4

A: Topic:- matrix

Q: Given the solution matrix from the calculator, write the solution 1 0 | 5 0 1 | -6What's the correct…

A: 1) The given matrix represents a system of linear equations in two variables, typically denoted as x…

Q: Write an augmented matrix for the system of equations. 7x + 6y = 74   9y = 27

A:

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.