(1 point) Give a 3 x 3 elementary matrix E which will carry out the row...

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(1 point) Give a 3 x 3 elementary matrix E which will carry out the row operation (-9)R₁ → R₁. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix 5 -1 2 -2 4 2 -4 4 EA = A = -3 2 -3 (1 point) Give a 3 x 3 elementary matrix E which will carry out the row operation R₂ → R3. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix -5 1 3 2 -2 5 4 -5 EA = A = 2 -2 -2 -3 (1 point) Give a 4 x 4 elementary matrix E which will carry out the row operation R3 + 5R₂ → R3. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix -2 -5 EA = A = 15 1 5 5 3 3 -2 (1 point) Consider the following Gauss-Jordan reduction: Find E₁ = = 1 -7 1-3 0 **----- 0 0 -6 0 1 0 -3 21 -6 0 1 1 -3 0 -7 21 -6 0 1 0 A -1 -1 Write A as a product A = E¹ E₂¹ E3¹ E¹ of elementary matrices: E₁ A 1000 -3 0 1 1 0 Ę₂ E₁ A 1 0 0 00 1 0 10 H H H Ez E₂ E₁ A 01 00 0 0 = I 1 E₂ E3 E₂ E₁ A (1 point) Find a non-zero, 2 x 2 matrix such that: -7 -6 21 18 * 00 [8] (1 point) Solve for X. X II 6 2] x + [$]=[ 3]-[81] X (1 point) Assume that A is a matrix with three rows. Find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed. -7R3 + R₂ ⇒ R₂ -5R₁ ⇒ R₁ B = (1 point) Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. Then find E-¹ and give the elementary row operation corresponding to E-¹ -5R₂ ⇒ R₂ E = E-1 = The elementary row operation corresponding to E-¹ is: A. Ro⇒ R₂ B. R₂ R₂ C. R₂ + R₁ ⇒ R₂ D. -5R₂ ⇒ R₂ E. Ro⇒ Ro (1 point) Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. Then find E-¹ and give the elementary row operation corresponding to E-¹. R3 ↔ R₁ E = E = The elementary row operation corresponding to E-¹ is: OA. R3 ⇒ R₂ B. R₂ R₁ C. R₁ R₂ (1 point) Give a 3 x 3 elementary matrix E which will carry out the row operation (-9)R₁ → R₁. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix 5 -1 2 -2 4 2 -4 4 EA = A = -3 2 -3 (1 point) Give a 3 x 3 elementary matrix E which will carry out the row operation R₂ → R3. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix -5 1 3 2 -2 5 4 -5 EA = A = 2 -2 -2 -3 (1 point) Give a 4 x 4 elementary matrix E which will carry out the row operation R3 + 5R₂ → R3. E = Test that E actually works for carrying out this row operation by computing the product EA for the matrix -2 -5 EA = A = 15 1 5 5 3 3 -2 (1 point) Consider the following Gauss-Jordan reduction: Find E₁ = = 1 -7 1-3 0 **----- 0 0 -6 0 1 0 -3 21 -6 0 1 1 -3 0 -7 21 -6 0 1 0 A -1 -1 Write A as a product A = E¹ E₂¹ E3¹ E¹ of elementary matrices: E₁ A 1000 -3 0 1 1 0 Ę₂ E₁ A 1 0 0 00 1 0 10 H H H Ez E₂ E₁ A 01 00 0 0 = I 1 E₂ E3 E₂ E₁ A (1 point) Find a non-zero, 2 x 2 matrix such that: -7 -6 21 18 * 00 [8] (1 point) Solve for X. X II 6 2] x + [$]=[ 3]-[81] X (1 point) Assume that A is a matrix with three rows. Find the matrix B such that BA gives the matrix resulting from A after the given row operations are performed. -7R3 + R₂ ⇒ R₂ -5R₁ ⇒ R₁ B = (1 point) Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. Then find E-¹ and give the elementary row operation corresponding to E-¹ -5R₂ ⇒ R₂ E = E-1 = The elementary row operation corresponding to E-¹ is: A. Ro⇒ R₂ B. R₂ R₂ C. R₂ + R₁ ⇒ R₂ D. -5R₂ ⇒ R₂ E. Ro⇒ Ro (1 point) Assume that A is a matrix with four rows. Find the elementary matrix E such that E A gives the matrix resulting from A after the given row operation is performed. Then find E-¹ and give the elementary row operation corresponding to E-¹. R3 ↔ R₁ E = E = The elementary row operation corresponding to E-¹ is: OA. R3 ⇒ R₂ B. R₂ R₁ C. R₁ R₂