Let W be a subspace of the space mathbb{R}^{4} with standart inner product. Let S=left{left[begin{array}{l}1 1 1 1end{array}right],left[begin{array}{c}-1 4 4 1end{array}right]right} be a basis for W. Use the Gram-Schmidt process to transform the basis S into an orthonormal basis.

Question

Let W be a subspace of the space mathbb{R}^{4} with standart inner product. Let S=left{left[begin{array}{l}1  1  1  1end{array}right],left[begin{array}{c}-1  4  4  1end{array}right]right} be a basis for W. Use the Gram-Schmidt process to transform the basis S into an orthonormal basis.

Accepted Answer

Step:1 ：Apply the Gram-Schmidt process to the given basis S: (S = left{begin{bmatrix}1  1  1  1end{bmatrix}, begin{bmatrix}-1  4  4  1end{bmatrix}right})Step:2 ：Normalize the orthogonal vectors to obtain the orthonormal basis: (left{begin{bmatrix}0.5  0.5  0.5  0.5end{bmatrix}, begin{bmatrix}-0.70710678  0.47140452  0.47140452  -0.23570226end{bmatrix}right})Step:3 ：boxed{text{Final Answer: } left{begin{bmatrix}0.5  0.5  0.5  0.5end{bmatrix}, begin{bmatrix}-0.70710678  0.47140452  0.47140452  -0.23570226end{bmatrix}right}}

Answer

Step: 1 ：Apply the Gram-Schmidt process to the given basis S: (S = left{begin{bmatrix}1  1  1  1end{bmatrix}, begin{bmatrix}-1  4  4  1end{bmatrix}right})Step: 2 ：Normalize the orthogonal vectors to obtain the orthonormal basis: (left{begin{bmatrix}0.5  0.5  0.5  0.5end{bmatrix}, begin{bmatrix}-0.70710678  0.47140452  0.47140452  -0.23570226end{bmatrix}right})Step: 3 ：boxed{text{Final Answer: } left{begin{bmatrix}0.5  0.5  0.5  0.5end{bmatrix}, begin{bmatrix}-0.70710678  0.47140452  0.47140452  -0.23570226end{bmatrix}right}}

Let $W$ be a subspace of the space $R^{4}$ with standart inner product. Let $S = {[\begin{array}{l} 1 \\ 1 \\ 1 \\ 1 \end{array}], [\begin{matrix} - 1 \\ 4 \\ 4 \\ 1 \end{matrix}]}$ be a basis for $W$ . Use the Gram-Schmidt process to transform the basis $S$ into an orthonormal basis.

Answer

Popular Problems

Let W be a subspace of the space R4 with standart inner product. Let S={[1111],[−1441]} be a basis for W. Use the Gram-Schmidt process to transform the basis S into an orthonormal basis.

Answer

Popular Problems

Let $W$ be a subspace of the space $R^{4}$ with standart inner product. Let $S = {[\begin{array}{l} 1 \\ 1 \\ 1 \\ 1 \end{array}], [\begin{matrix} - 1 \\ 4 \\ 4 \\ 1 \end{matrix}]}$ be a basis for $W$ . Use the Gram-Schmidt process to transform the basis $S$ into an orthonormal basis.