Find the vector \$x\$ determined by the given coordinate vector \$_B\$ and given basis \$B\$: \$\$ B = left eginbmatrix 3 \ -5 endbmatrix, eginbmatrix -4 \ 6 endbmatrix ight, quad _B = eginbmatrix 5 \ 3 endbmatrix.\$\$

I observed a couple different means to method this problem from tutorials on YouTube, and also each resulted in a different answer. This is what I got:

3 -4 | 5-5 6 | 33 * 5 + -4 * 3 = 3-5 * 5 + 6 * 3 = -7A = 3 -7v1 = 3 -5v2 = -4 63 * v1 + -7 * v2 = x= 9 + 28 -15 -42= 37 57Is that the correct answer?

You are watching: Find the vector x determined by the given coordinate vector  This is greatly a matter knowledge the definition and notation. Usually if you have actually a basis \$B= astecraftedmcd.combf v_1, astecraftedmcd.combf v_2 \$ and are told that \$< astecraftedmcd.combf x>_B = (x_1, x_2)\$ for genuine numbers \$x_1\$, \$x_2\$, then \$ astecraftedmcd.combf x = x_1 astecraftedmcd.combf v_1 + x_2 astecraftedmcd.combf v_2\$. In our particular instance, \$\$ astecraftedmcd.combf x=5v_1 + 3v_2 = 5(3, -5) + 3(-4, 6) = (15, -25) + (-12, 18) = (3, -7) = 3 astecraftedmcd.combf e_1 - 7 astecraftedmcd.combf e_2\$\$ wright here \$ astecraftedmcd.combf e_1 = (1, 0)\$ and \$ astecraftedmcd.combf e_2 = (0, 1)\$ are the traditional basis vectors for \$ astecraftedmcd.combb R^2\$. Thanks for contributing a solution to tastecraftedmcd.comematics Stack Exchange!

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