Question

Let A be a square matrix with an inverse A-1. Show that if Ab = 0...

Let A be a square matrix with an inverse A-1.

Show that if Ab = 0 then b must be the zero vector.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
let A,B be invertible matrix (AB^-1 - I)^-1 = 4B^TA^-1 Find A inverse, which should have...
let A,B be invertible matrix (AB^-1 - I)^-1 = 4B^TA^-1 Find A inverse, which should have an expression in terms of B
A) Find the inverse of the following square matrix. I 5 0 I I 0 10...
A) Find the inverse of the following square matrix. I 5 0 I I 0 10 I (b) Find the inverse of the following square matrix. I 4 9 I I 2 5 I c) Find the determinant of the following square matrix. I 5 0 0 I I 0 10 0 I I 0 0 4 I (d) Is the square matrix in (c) invertible? Why or why not?
(a) Find the inverse of the following square matrix. I 5 0 I I 0 10...
(a) Find the inverse of the following square matrix. I 5 0 I I 0 10 I (b) Find the inverse of the following square matrix. I 4 9 I I 2 5 I (c) Find the determinant of the following square matrix. I 5 0 0 I I 0 10 0 I I 0 0 4 I (d) Is the square matrix in (c) invertible? Why or why not?
7) Let B be a matrix with a repeated zero eigenvalues. Then show that B2 =...
7) Let B be a matrix with a repeated zero eigenvalues. Then show that B2 = 0 (the 2 × 2 zero matrix). Use this to show: if A has a repeated eigenvalue λ0, then (A − λ0I) 2 = 0. (Hint: Use the fact that Bv = 0 for some nonzero vector v)
Show that a square matrix P over the integers has an inverse with integer entries if...
Show that a square matrix P over the integers has an inverse with integer entries if and only if P is unimodular, that is, the determinant of P is ±1.
1). Show that if AB = I (where I is the identity matrix) then A is...
1). Show that if AB = I (where I is the identity matrix) then A is non-singular and B is non-singular (both A and B are nxn matrices) 2). Given that det(A) = 3 and det(B) = 2, Evaluate (numerical answer) each of the following or state that it’s not possible to determine the value. a) det(A^2) b) det(A’) (transpose determinant) c) det(A+B) d) det(A^-1) (inverse determinant)
A square matrix A is said to be idempotent if A2 = A. Let A be...
A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. Show that I − A is also idempotent. Show that if A is invertible, then A = I. Show that the only possible eigenvalues of A are 0 and 1.(Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.) Let W = col(A). Show that TA(x) = projW x and TI−A(x)...
A square matrix A is said to be idempotent if A2 = A. Let A be...
A square matrix A is said to be idempotent if A2 = A. Let A be an idempotent matrix. Show that I − A is also idempotent. Show that if A is invertible, then A = I. Show that the only possible eigenvalues of A are 0 and 1.(Hint: Suppose x is an eigenvector with associated eigenvalue λ and then multiply x on the left by A twice.) Let W = col(A). Show that TA(x) = projW x and TI−A(x)...
Given the following vector X, find a non-zero square matrix A such that AX=0: You can...
Given the following vector X, find a non-zero square matrix A such that AX=0: You can resize a matrix (when appropriate) by clicking and dragging the bottom-right corner of the matrix. x = [-1] [10] [-4] This is a 3x1 matrix.
Show that if a square matrix K over Zp ( p prime) is involutory ( or...
Show that if a square matrix K over Zp ( p prime) is involutory ( or self-inverse), then det K=+-1 (An nxn matrix K is called involutory if K is invertible and K-1 = K) from Applied algebra show details
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT