6 CO -3 -1 LetA= -9 0 and B= - 8 9 Solve the matrix equation 4A + 5B = 3X for X. -1 -1 5 an X = (Type an integer or simplified fraction for each matrix element.)
Let A and B be 3x3 matrices, with det A=9 and det B = - 6. Use properties of determinants to complete parts (a) through (e) below. a. Compute det AB. det AB = (Type an integer or a fraction.) b. Compute det 5A. det 5A = (Type an integer or a fraction.) c. Compute det BT. det BT = (Type an integer or a fraction.) d. Compute det A-7. - 1 det A (Type an integer or a simplified...
Let A be a 2x2 matrix with eigenvalues 4 and and corresponding eigenvectors V, = and v2 Let} be a solution of the difference equation X: 1 -AX. Xo' - a Computex, = Ax (Hint: You do not need to know itselt b. Find a formula for x, involving k and the eigenvectors V, and v2 a x Ax=(Type an integer or simplified fraction for each matrix element) b. xxv.v2 (Type expressions using k as the variable.)
A matrix A and an echelon form of A are shown below. Find a basis for Col A and a basis for Nul A 1 15 19 -2-7 1 15 19 0 5 -1 10 16 2 2 0 5 70-1 -2-5-3 49 0 0 01 6 3 25 29-5-11 0 0 00 0 A- Find a basis for Col A (Use a comma to separate answers as needed. Type an integer or simplified fraction for each matrix element.) Find...
Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector orthogonal to W. 1 -1 6 u u2 6 1 1 4 1 y= (Type an integer or simplified fraction for each matrix element.)
a. Compute det \(\mathrm{AB}\).det \(\mathrm{AB}=\square\) (Type an integer or a fraction.)b. Compute det \(5 \mathrm{~A}\).det \(5 \mathrm{~A}=\square\) (Type an integer or a fraction.)c. Compute det \(\mathrm{B}^{\top}\).\(\operatorname{det} \mathrm{B}^{\top}=\square\) (Type an integer or a fraction.)d. Compute \(\operatorname{det} A^{-1}\).\(\operatorname{det} \mathrm{A}^{-1}=\square\) (Type an integer or a simplified fraction.)e. Compute det \(\mathrm{A}^{3}\).det \(\mathrm{A}^{3}=\square\) (Type an integer or a fraction.)
a b 1 d-b - lz and A-'A-Iz. Use the fact that if A- then A to find the inverse of the matrix, if possible. Check that AA ad-bc cd -C a - 2-3 4 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. OAA? (Type an integer or a simplified fraction for each matrix element.) O B. The matrix does not have an inverse.
Solve the matrix game. 5 0 1 -3 7 4 PE (Type an integer or simplified fraction for each matrix element.)
Solve the matrix game. -2 3-1 -1-2-3 -3-1 3 The optimal strategy for the tow player is P- (Type an integer or simplified fraction for each matrix clement.) The optimal strategy for the column player is 0-0 (Type an integer or simplified fraction for each matrix element.) The value for the game is v (Type an integer or a simplified traction)
X1 Let x = V = and v2 - and let T: R2R2 be a linear transformation that maps x into xxv, + XxV2. Find a matrix A such that T(x) is Ax for each x. X2 A= Assume that is a linear transformation. Find the standard matrix of T. T:R3-R2, T(41) = (1,3), and T(62) =(-4,6), and T(03) = (3. – 2), where e1, 22, and ez are the columns of the 3*3 identity matrix. A= (Type an integer...